Schrödinger’s Rabbits: The Many Worlds of Quantum [1st ed.] 0309090512, 978-0309090513

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SCHRODjNGpR'S RABBITS

the

many worlds

D

COLIN BRUCE

of

quantum

SCHRODINGER'S RABBIT sl^ or the better part of a century, attempts

F

the

in

quantum world seemed doomed

to

really

advances

technological

recent

But

failure.

what was

going on

to explain

have made the question both practical and

A

urgent.

Oxford University have

physicists at

the challenge. This

At

long

to

think

last,

in

risen to

their story.

is

there

sensible

a

is

about quantum

new view

group of

imaginative

brilliantly

way

mechanics.

The

abolishes the need to believe

randomness, long-range spooky forces,

or

powers life

or death.

comes

we

collapse

to

at

live

In

cats

into

a

of

state

new understanding

But the

we

a price:

mysterious

with

observers

conscious

must accept that

a multiverse wherein countless

versions of reality unfold side-by-side. The

philosophical

and personal consequences

of this state of affairs are awe-inspiring.

The

new

interpretation

Imaginative

physicists

new

wonderful devices

that

initially

conceive

of

measuring

share

information

between worlds and

calculations.

to

technologies:

effectively

borrow the power

allowed

has

computers

that

can

of other worlds to perform

by

Step

step,

the

problems

associated with the original many-

worlds formulation have been addressed and

answered so picture has

Just

that

a clear but

startling

new

emerged.

as Copenhagen

was the centre of quantum

discussion a lifetime ago, so Oxford has been the epicenter of the

modern debate, with such

(continued on back flap)

#

A

'4

9U

V

Digitized by the Internet Archive

2016

in

^

4

https://archive.org/details/isbn_9780309090513

SCHRODINGER’

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Schrodinger which Erwin Schrodinger developed the wave-theory formulation, with triumphant described the previously mysterious hydrogen atom was as Schrodinger’s interpretation of his wave mechanics accuracy.

simple as ality

duwas bold. His answer to the problem of wave-particle wave there are no particles, only waves. Just as a tsunami

it

was that

can rise and spread out invisibly thinly in the deep ocean, but debecome concentrated as it passes over shallow water, ultimately

may be

positing

most of its energy on

wave can vary

greatly in

its

a

narrow stretch of coast, so any kind of

physical extent. Schrodinger thought that

and matter were merely manifestaas when a water wave tions of waves squeezed to an extreme degree and by the shape of an estuary rears up to a sudden peak

the apparent particles of radiation

—

focused

expends

energy in knocking

all its

down a tall lighthouse, for example.

Schrodinger’s view works quite well for

bound

particles,

such as

whose behavior is described by the time-indeto answer pendent” Schrodinger equation, which does not even try any given instant. But it the question of where the particle is located at

electrons in an atom,

works much

less well for particles in free space,

such as an isolated

the equation proton or electron. Then the time-dependent version of anything, the wave predicts that as long as it is not interacting with will

extendcontinue to gradually flatten and spread out, in principle

interaction somewhere ing to infinity. Yet even a tiny observation-like volume of space can bring an extremely pointlike electron in this

small to measpringing into view, with dimensions that remain too

sure— and

this

happens

in less

time than

the region of space where, until that

would take

light to cross

moment, we thought

the electron

hard to imagine any reasonable physimechanism that could bring about quantum collapse in this kind

might cal

it

be.

As we have seen,

of nonlocal case.

it is

The Old Testament / 59

Schrodinger did not claim to have an answer to the problem, but

he did make clear his contempt for the idea, which underpins several of the interpretations described below, that a system might be regarded as not

having a definite

that this notion

state until

makes sense

an observation

is

made.

If

we accept

in the context of microscopic systems,

Schrodinger argued, then in the appropriate circumstances have to apply to larger systems as well

Suppose you constructed placed within

soon

as the

filter

and

it

box was

kill

and

a cat

if

living things

such as

a sort of Russian roulette device which, as

would

the photon

photon toward a polarizing

fire a

happened

to pass through.

a fundamentally unpredictable 50 percent chance that the

pass through the

filter.

By the “nothing

ment, the cat would have no definite

maybe hours later, to

cats.

box and

a completely observation-proof

sealed,

the cat

—even

would

it

reveal either a

is

photon

is

will

actual until observed” argu-

state until the

dead

There

cat

box was opened,

with rigor mortis or a

live

but hungry one. Schrodinger invented his famous parable of the catin-a-box not to be believed, but to be disbelieved, as a reductio ad ab-

surdum.

He thought

terms that the cat

is

that

it

was manifestly ridiculous

neither dead nor alive until the

to think in the

box

is

opened.

Born Max Born had saw them

as

an alternative way to look

waves of probability.

It

will

at

Schrodinger’s waves.

be useful to us

understand the modern philosophy of probability, and for

and

for the sake of clarity,

I

shall extrapolate his

later

this

on

He to

reason

argument into mod-

ern terminology and examples.

There

is

a subtle difference

between probability and

statistics.

Consider the difference between the two following questions:

“There are 100 people sticker placed

on

in this hall. Fifty

their backs.

What

of them have had a white

percentage have white stickers on

their backs?”

and

“I

have selected

at

random someone from the hall who now stands

60

/ Schrodingers Rabbits %

before you.

What

bears a white the chance that this person’s back

is

Sticker?”

The answer

to the fir^questio'n

The second question

is

straightforward: 50 percent.

trickier. After all,

is

the person standing before

everyone in the audience except either has a sticker or doesn’t. If else in the room already you can see the subject’s back, then everyone this person’s back” is knows that the hypothesis “There is a sticker on

you

or false with 100 percent cereither true with 100 percent certainty

probable

“50 percent what sense can it be correct to answer when you consider that The matter becomes even more puzzling you hesitate to answer the second the probability can change. Suppose “1 will give you some further question and the host goes on to say, them had white are 50 women in the hall and 40 of ?

tainty. In

information. There stickers placed

uted

on

among the

You can

their backs.

50 men.”

see that the person before

able to revise your estimate rational to

do

10 stickers were distrib-

The remaining

that?

upward

The person

you

is

a

woman, so

to 80 percent. But

it is

reason-

how can

it

be

before you has not changed, nor has

the fact that she either has a sticker

on her back or has

not.

How can

the right answer have changed?

The answer that probability rational for

when you

you

give is most philosophers of mathematics would ignorance. It is not best thought of as a measure of

that is

a situation change to think that the physical facts of information, but it is rational for you to uke

are given

new

ignorance. That this is not a trivial into account your reduction of Monty Hall problem, in which a distinction is shown by the famous following shows you three cabinets, and gives you the

game show host information: “One of these

cabinets contains

one million

dollars.

The

one of the cabinets. I will open one of “Then, just to keep the audience entertained, empty. I will always choose an the other cabinets and reveal that it is choice. After that 1 will empty cabinet to open, and never your original

other two are empty.

I

will ask

you

to choose

original choice or to you the opportunity either to stick with your cabinet. I will open whichever of switch it to the remaining'unopened

give

the

two cabinets you have

dollars, the

money

is

finally chosen. If

yours.”

it

contains the million

The Old Testament / 61

The game

starts,

and you choose the left-hand cabinet. The host

opens the right-hand one and shows question that confronts you

Or does

the middle cabinet?

Ts

is, it

it

it is

empty. The million-dollar

worth changing your choice

make no

to

difference to your chance of

Winning?

Most people (including incorrectly lines;

‘The

when

fact

they

physicists

meet

first

this

and mathematicians) reason problem, along the following

of whether the middle cabinet contains the

money can-

not have changed as a result of all this flim-flam. Therefore, there rational reason to nets; there

is

my

change

choice. There are

an equal chance that the money

is

is

no

two unopened cabi-

in either.’

But they are profoundly mistaken. Because although the physical situation has not changed, your ignorance has reduced

make

it

—and

that can

quite rational to change your choice. Your ignorance about

whether the money has not changed.

is

in

your original choice of the left-hand cabinet

It is still

a one-third chance, as

it

was

at the start

of

the game. But your ignorance about which of the other two cabinets

has the money, assuming you originally guessed wrong, has disappeared.

and

The chance

in that case the

that

you

originally guessed

money must be

in the

wrong

is

two-thirds,

middle cabinet. You double

your chances of winning by switching your choice. Thus a change in

— happens when you make meayour expectation of the quantum system — can

your knowledge of the universe

surement of a

a

as

revise

probable results you will get from subsequent measurements. To a naive

person

this

might look

as

though acquiring knowledge about the

system actually changed the system

this

a two-thirds

implied that

chance of winning, and then

first

probability are

still

is

greatly respected.

The

widely referred to as Born

have already seen, the most troubling observer

cabinet to an-

effect,

rules of

rules.

the

quan-

But as we

EPR paradox

by the Bell-Aspect experiment and the lottery cards,

cannot be explained by mere reduction of ignorance universe.

thinking that

measurement.

Born’s approach was and

as illustrated

falsely

money sometimes jumped from one

other as a result of their

tum

on the Monty Hall

like guests

that changing their initial choice did indeed give

show discovering them

—

in a classical

62

de

/ Schrodingers Rabbits

Broglie

and

Einstein

proposed in 1926 by Louis Albert Einstein initially preferred an idea radiation and matter are real Broglie. In this model the particles of de

and pointlike (or

at

any

rate,

very small) and their wavelike behavior

is

which

is

explained by their association with a kind of detectable only through

its

effect

on

phantom

particles.

This

is,

field,

of course, the

explain a great deal concept of guide waves. As we have seen, you can some kind of invisible fine of what goes on in quantum by postulating world that can guide and jostle particles in a wavestructuring to the like

manner, describable by mathematicians

in

terms of hidden local

variables.

However, Einstein soon came to

realize the

huge

difficulties that

most famous scientific nonlocality posed for this picture. In one of the papers of

time, written with Boris Podolsky

all

and Nathan Rosen, he

particles have in some described the nub of the problem: After two appears and traveled far apart, measuring one of them

way

interacted

to have an instant effect

ever since as the Einstein

on

the other.

The problem has been known

EPR paradox, or simply EPR.

hoped

would turn out not

for a simple solution:

Such long-range

effects

quantum theory was incomplete more likely, there was some kind of er-

to exist. Either

and required modification

or,

“spooky forces” were operror in thefeasoning that implied that such special relativity implied that no ating. Einstein clearly thought that irrespective of any kind of influence could travel faster than light, quibbles about whether

was

could transmit information.

say easy to borrow a glib psychologist’s phrase and posidenial but at the time it was a perfectly reasonable

Nowadays, that he

it

in

it is

relativity, which had been tion to prefer the implications of special the time he was thoroughly tested, to those of quantum theory. At

pondering these matters there

was no

practical

in the 1930s

way to

(and even when he died in 1954),

investigate the matter experimentally. It

theoretical basis was not until the 1960s that John Bell formulated the definitive and practicable, and for an experiment that would be both were able to turn the not until the 1980s that Alain Aspect and others has been done experiment into foolproof'hardware. But now the test is real. many times, and there is no question about it.' Nonlocality

Einstein

was wrong. %

The Old Testament / 63

Bohr Niels

Bohr

is

interpretation. tion,

remembered

generally

Many

'

as the father of the

Copenhagen

textbooks describe the Copenhagen interpreta-

formulated in dialogues between Bohr and others in and around

Danish

that picturesque

city, as

being the orthodox or mainstream

quantum mechanics. Yet there is no general agreement on what the Copenhagen interpretation actually is. At the lowest common denominator, it can be summed up in the following pair of

interpretation of

statements:

The only

1.

of experiments as mea-

real things are the results

sured by conscious, macroscopic observers; there

is

no deeper under-

lying reality.

Experiments yield

2.

with either wavelike be-

results consistent

havior or particle-like behavior, depending on the design of the ex-

periment, but never both at the same time.

But until the Copenhagen interpretation came along, the whole point of doing experiments was to formulate a picture of an underlying this

Why, exactly, are we being forbidden to speculate further in instance? Surely the idea that there are questions that must not be

reality.

asked

is

contrary to the whole spirit of scientific endeavor.

Of course, there is nothing unreasonable about saying that a question is unanswerable because the result you get depends on the way that the question

asked. Consider, for example, a

is

with a thixotropic fluid but

—one

that acts like a liquid

like a solid if struck hard.

The question “Are

bag liquid or solid?” can be answered only is

filled

under gentle forces

the contents of this

in the context of whether

it

going to be squeezed or struck. But of course we can and do ask

questions

like:

Wily does level?

this

What

is

the threshold at which the behavior changes?

happen? What,

exactly,

is

going on

Bohr, by contrast, seemed to dismiss

quantum IS

punchbag

many

at the

molecular

questions about

as altogether meaningless, analogous to asking:

“What

color

up? Evidently Bohr

lated could

answer

felt all

confident that

quantum theory as then formu-

the questions that he

felt it

needful to ask of

it.

But he resisted further probing with wordy statements that have led

64

/ Schrodingers Rabbits X

“N

many

that the tougher to retreat in confusion ever since, convinced had dared to pose had indeed been foolish. To me,

questions they

of those Buddhist Bohr’s attitude seems uncomfortably reminiscent with the response sages who feel free To reply to ceiitain questions

“Mu!” which means “The question

unsaid!” But

is

many

people have

such gurus.

faith in

My views

on Bohr have

recently

an intriguing paper by

result of

undergone

Don Howard,

change

a partial

first

as a

delivered at a con-

Howard argues plausibly that the so-called unified by Copenhagen interpretation was a myth invented retrospectively

ference in Oxford.2

school of thought), Bohr’s enemies (or at any rate, enemies of his being intenHeisenberg and Popper. In Howard’s view, Bohr, far from tionally mystical in his replies, right, the nature of Bohr’s

was merely being

caution

many people will have heard

dote

child, a physicist,

and

is

careful. If

is

by an anec-

perfectly described

in different forms. In

Howard

my version, a

passing a philosopher are traveling in a train

through a country none of them has previously

visited.

The tram

passes a field in which they see a black sheep.

“Wow,”

in this counsays the child, “look at that. All of the sheep

try are black!”

The

physicist smiles.

really tell

is

that

know

at least

one

is

don’t

some of the sheep

The philosopher really

“We

smiles.

that at least

“We

know

in this

don’t

one sheep

that,

he

says.

All

we can

country are black.”

know

in this

that,

he

says.

All

we

country appears black on

side!”

we might consider that the physicist was three. But if we are visiting a truly unfamiliar

In an everyday context,

the

most

place

sensible of the

—such

as the

world of quantum

—then the philosopher’s point

directly you should make statements only about the things you inferences, is perceive, avoiding even the most reasonable-seeming sure will you gain logical. Only by sticking to what you know for

that

quite

a reliable understanding.

When Bohr insisted that all it is legitimate to say about a quantum experiment

opposed

to

cording to

“The experiihenter observes such-and-such “The quantum^ system was in such-and-such

is:

Howard he was merely being

result,” as state,

ac-

as careful as the philosopher

The Old Testament / 65

He

in the train story.

certainly

was not assigning any mystically pow-

erful role to conscious observers. Interpreting

“Conscious observers are the agents collapse”

would then be

as

who

any of his statements

as

quantum

physically trigger

much of a blunder as the famous mistrans-

lation of the canali (channels) that the astronomer^S^hiaparelli

thought he had seen on Mars as “canals,” implying that Schiaparelli was postulating intelligent (and presumably conscious) Martians as the agents that created them. I

tic,

accept Howard’s claim that Bohr was, at worst, a cautious agnos-

rather than a mystic. Possibly he

hoped

that

if

other investigators

followed his example of making statements about only what they observed, rather than

what they presumed, then a

of quantum would ultimately emerge. But to of cowardice about his stance.

It

fully objective picture

me

there seems a touch

was certainly frustrating

Bohr; famously, he once reduced Heisenberg to

to talk to

Here

tears.

is

an ex-

ample of a genuine Bohr statement quoted by Howard: The quantum

postulate implies that any observation of atomic

phenom-

an interaction with the agency of observation not to be neglected. Accordingly, an independent reality in the ordinary physical sense can neither be ascribed to the [atomic] phenomena nor to the agen-

ena

will involve

cies

of observation

This situation has far-reaching consequences.

On

one hand, the

defini-

tion of the state of a physical system, as ordinarily understood, claims the elimination of all external disturbances. But in that case, according to the

quantum

postulate,

any observation

the concepts of space

hand,

if

in order to

and time

will

lose their

make observation

be impossible, and, above

immediate

possible

sense.

we permit

On

all,

the other

certain interac-

tions with suitable agencies of measurement, not belonging to the system, an unambiguous definition of the state of the system is naturally no

longer possible, and there can be no question of causality in the ordinary sense of the word. The very nature of the quantum theory thus forces us

and the claim of causality, the union of which characterizes the classical theories, as complementary but

to regard the space-time co-ordination

exclusive features of the description, symbolizing the idealization of ob-

servation and definition respectively. If

you find

this less

than transparent, you have

my

sympathy.

It

sounds rather deep. But try rereading the passage, changing the words “quantum” to “Olympian” and “atomic phenomena” to “gods,” and

you

will see just

how

unsatisfactory the above statement

is.

66 / Schrodingers Rabbits

Bohr’s answer to the specific problem of wave-particle duality particularly inadequate.

He

said, essentially,

no more than

that

is

we

should expect a particle-like result from a particle-oriented experime, ment, and a wavelike result from a wave-oriented experiment. To this

uncomfortably suggestive of an engineer’s rule-of-thumb. Imag-

is

ine that

you meet

a hydraulics engineer

who

tells

you the following

story:

“I

have two formulas that

through a channel of given

tell

size,

me

exactly

how fast

water will flow

under a given pressure

difference, he

“One formula works well for flow through narrow pipes, as used domestic plumbing. The other formula works well for large con-

says.

in

structions, like canals

and aqueducts.”

take a look at his formulas. “But these are two completely describing the different equations!” you exclaim. “They are supposedly

You

same thing, but would predict completely different results if they were applied to the same channel. What happens in a pipe of intermediate size,

say one that

is

10 centimeters in diameter?”

The engineer shrugs and

canals,”

his shoulders.

he says cheerfully.

intermediate

“I don’t

I

do only domestic plumbing

need to know the answers for

sizes.”

Apart from his lack of theoretical

curiosity, this hypothetical engi-

neer would be missing out on his appreciation of a most important phenomenon: turbulence. The different equations arise because the

whereas flow through a narrow tube tends to be smooth or laminar, turbularger flows naturally break up into the swirls and eddies of lence. est;

Understanding turbulence

is

not only of great theoretical inter-

manipulating the conditions that trigger

its

onset

is

the key to

harnessing the properties of fluid flow in all sorts of contexts. Nowadays, we can do experiments involving behavior that termediate between particle-like and wavelike.

We

is

in-

are beginning to

understand a process called decoherence, which is arguably the real mechanism of quantum collapse and is in some ways quite analogous to turbulence. situations.

Bohr has absolutely nothing

Agnosticism

is

to say

about these kinds of

perhaps an intellectually respectable posi-

does not lead to progress. Bohr had not so much an interpretation of quantum mechanics as an absence of one.

tion,

but

it

The Old Testament / 67

The worst

part of the

Copenhagen

and comfort

tinues to give aid

legacy, though,

to those

who,

is

that

in the debate

it

con-

between

and philosophers over the meaning of quantum theory, could be described as at the extreme philosophical end of the spectrum those who maintain that questions about reality beyond the

physicists

—

scope of immediate personal observation are meaningless. This solipsist

viewpoint

is

impossible to refute, just like such claims

have actually been lying on a couch reality

your

life,

You

wired up to a virtual

machine,” or “The world, complete with your memories and

those of everybody is

all

as.

utterly barren

else,

has just been created in the

and unhelpful to the

ingful picture of the universe.

scientist’s

last

second.” But

quest to build a

As Howard has pointed out,

it

mean-

this idea

has remained in the running largely because various claimants have

muddied Bohr’s name by falsely associating him with in a Copenhagen synthesis that never was.

this

viewpoint

von Neumann and Wigner The mathematician John von Neumann’s major contribution to the world was to lay the foundations for the computer revolution that followed later in the 20th century. But he also worked on the quantum theory, ics,

and

his

book. Mathematical Foundations of Quantum Mechan-

published in 1932, was fundamental to the

field.

Von Neumann was the first person to think really deeply about the problem of quantum collapse. He was troubled by the potential for infinite regress, which we have already come across. If system A is measured by being put

in contact with a larger system B, the result

measured by being put

in contact with a

forth,

OK,

where does the process stop?

that’s

it,

and

settle

down

still

When

larger system C,

cal

and so

does the universe decide,

to a particular version of reality rather

than tracing out yet more families of wavy variants? identified a physical

Von Neumann

need for collapse that goes beyond the philosophi-

problem of why we observe a

realized that the equations of

single fixed version of reality.

quantum

example.

He

are time symmetric. This, of

course, contrasts with our macroscopic experience that there clearly defined

is

is

a

arrow of time; eggs do not unscramble themselves, for

68 / Schrodingers Rabbits

In the classical world, the arrow of time increase of entropy,

which can

is

associated with a steady

be understood as a decrease of

also

The universe started in an extremely ordared state, crammed remains tiny space, and^even today most of its visible mass

ordering. into a

occupying a Very small fraction of its overall volume. temperature difference between those stars and the cold empti-

packed into

The

stars

ness of interstellar

and

intergalactic space provides the flow of energy

that drives such processes as

But

how does

this tie in

life

on

Earth.

with the timeless quantum world, whose

mathematical waves flow symmetrically without anything correspondthat there is an ing to an arrow of time? Von Neumann worked out multiple entropy increase associated with quantum collapse, when interesting finding, possibilities reduce to a single outcome. This is an

but of course

it

requires physical collapse to occur at

some

point.

Von

Neumann reasoned that in the absence of any evidence for its happening earlier, the collapse should be

assumed

to take place at the point

where a conscious observer inspects a quantum system. To be fair to von Neumann, we must remember that he was writand before such basic thought experiments as Schrodingers cat ing

EPR had

even been formulated.

revised his views his granting

if

I

strongly suspect that he

he had lived until a

quantum

hand, and attributing

later era.

The

contrast between

collapse an important physical role it

to

would have

on the one

an almost mystical cause on the other,

is

But the idea of a conscious observer with a mysterious power strongly to a to collapse systems by looking at them has appealed so breed of thinker that it has survived for many decades. For

bizarre.

certain

example, von Neumann’s ideas were

still

being extended in the 1960s

by Eugene Wigner.

von Neumann’s hypothesis from four decat excades earlier should be taken literally. Thus in Schrodinger s periment, the point at which the cat’s fate is determined comes not

Wigner suggested

even

that

when the box is opened, but when

aware of the

result.

For example,

if

a conscious observer

the cat

box

is

becomes

in space out

beyond

an unmanned p/obe with an automated opening mechanism that reveals the box’s interior to a television camera, the cat’s fate

Pluto, aboard

is

not decided until the

TV signal reaches the inner solar system. How-

The Old Testament / 69

an astronaut observer has been sent out to watch from aboard a nearby spacecraft, the cat’s fate is decided as soon as he can see it, microseconds after the box opens. This is known as the paradox of

ever, if

Wigner’s friend. (One wonders what he proposed doing to his en^'4

“

emies.)

^

Wigner’s ideas have been rightly lampooned, by John Bell among others. Among the reductio ad ahsurdum questions one can ask are:

“What happens cat.

Does the

“What

if

there

is

a conscious observer in the

cat then die immediately, before the

box

exactly counts as a conscious observer?

scious observer? If so,

what about a mouse,

is

box with the opened?”

the cat a con-

Is

what

a frog, a slug? If not,

about a chimpanzee, or a Neanderthal? Where does the dividing

come? Does the observer need a PhD?” The beautiful point has been made ogy, there were

line

that in the context of cosmol-

no conscious observers

at all until a certain

(probably quite recent) in the universe’s history.

Was

point

the entire uni-

verse waiting to collapse into a definite state until the

first

ape-man

came along? Conscious observers with spooky powers to collapse systems up to the size of a universe seem rather implausible. In any case the conscious-observer-collapse hypothesis does nothing to resolve the real

problem of quantum, nonlocality. Remember the lottery cards example where my partner went to Mars. What happened when we simultaneously scratched our cards? Did my observation collapse the universe, or did hers, or was it both? In whichever case, the effect must

presumably have rippled out lottery card got to

faster

be the correct

than light to ensure that the far-off

color.

Bohm Other attempts to extend the early interpretations of quantum were more respectable. Perhaps the most heroic attempt to cling to a classian cal picture is found in the rather tragic story of David Bohm,

American

don when project.

physicist

who came

his services

to England’s Birkbeck College in

Lon-

were no longer required on the Manhattan

70 / Schrodingers Rabbits

(I

tists

cannot

resist

pointing out here a curious fact about the scien-

who have contributed the most to our understanding of quantum

remarkably high proportion have four^etter surnames beginning with “B ” Thosfe we^hall encounter include Born, Bohr, Bohm,

theory:

and

A

Bell; there

some claim

was

there

In the 1950s,

is

Bose of Bose-Einstein condensate fame. And nothing weird about the statistics of quantum!)

also

Bohm effectively rediscovered and revitalized the pi-

of a lot-wave theory which had been invented by de Broglie a quarter with century earlier, but fallen out of favor because of its problems nonlocality.

Bohm was

work somehow,

determined to make the pilot-wave theory

despite the apparent faster-than-light influences of

EPR. Mathematically, his work was to an extent successful and his findings interesting. after a fashion if

nitely

He

discovered that pilot-wave theory could

work

that the guide waves continued indefi-

you assumed

when they were no longer associated with any particular He found, however, that individual guide waves did not, as

even

particle.

you might expect,

away with time, viewed from

die

a macroscopic

water waves decaying to ripples after the storm that caused them has died down. The guide waves can remain large in amplitude even at times and places remote from their last occupation by a surf-

scale, like

ing particle.

One way

to see intuitively

that warships carry charts of equal scale

tion of the^world’s oceans

most unlikely

and

this

must be

required to navigate properly

waves,

is

if

if

is

to reflect

detail covering every por-

—because although there

to be ordered to,

visit frequently. Pilot

why

are places they are

they ever are, then the scale of maps

just the

they do

same

exist,

as for those regions they

must guide

particles

with

accuracy through low-probability as well as high-probability regions. Bohm’s (Ironically, as David Deutsch and others have pointed out,

work is

excellently supportive of

many- worlds.

If you forget

the rather

notion that the waves are occupied by surfers whose posipossible tions define a single reality, then the waves are tracing out all

artificial

come to this later.) Bohmian mechanics, as it is now called, is more sophisticated than

world-lines with equal

fidelity.

But we

shall

we constructed in the previous chappotential, his parters. Guided by an extra field he called the quantum undergoing ticles did not “tumble off” their guide waves on

the simple surfing-particle story

The Old Testament 1 71

measurement-like interactions; rather, the wave that they were riding

underwent

a subtle

But of course

and pseudo-instantaneous change.

this

quantum

potential has to operate in a nonlocal

manner, and Bohm’s attempts to explain

how

this

could happen be-

came rather desperate. In a book written with Basil HUe^ shortly bethe fore Bohm’s death (it was published posthumously), he introduces notion of implicate order.^ The attempt to understand this concept has baffled

many

separate ways.

physicists,

We

but

I

think the idea can be taken in two

can understand

it

as saying either that there

kind of limited but instantaneous linkage between verse,

which

is

all

is

a

parts of the uni-

not directly accessible from the macroscopic world

where time’s arrow operates, or that the universe contains embedded going on in in every part of itself encoded information about what is the other parts.

view we have already examined. They include contradictions with the spirit of special relativity, implying backward-in-time causation at the micro scale, as well as the truly

The problems with the

first

enormous amount of behind-the-scenes calculation that the universe must be assumed to do if every part of it can instantly affect every

The problem with the second view is that it implies predesmovie, If a billion projectors are playing exactly the same

other part. tination.

without needing to communicate with one another, then even if each projector is showing only one particular area of each frame at maxi-

mum same

magnification, they

must

surely

all

have been loaded with the

film at the start of the performance.

Price, Valentini,

and Cramer

nothing intrinsically impossible about predestination. Richard Feynman was struck by the symmetry between the processes by which radiation is absorbed and emitted. We normally think of radia-

There

is

tion as going out target

from

from only one

converging on

its

its

source in

direction; yet

target

from

tight with perfect precision.

all

all

it is

directions, but approaching a

just as reasonable to think of

directions,

Feynman and

an

invisible

it

noose drawn

others have toyed with the

universe idea that although, to our usual perception, the order of the

72

is

/ Schrodingers Rabbits

decreasing, perhaps in subtle ways

is

it

increasing.

The universe

originated in one rather special highly ordered state, and ing toward another, rather than toward pure disorder.

is

progress-

From our point

of view, this progress, tdward a future constraint looks exactly like predestination. As Professor Cope explained in Chapter 1, predestination

can easily account for

Indeed, predestination can in

EPR correlations.

phenomenon. Think of two conversation; if each knows ex-

principle explain any apparently nonlocal

people a light-year apart, holding a

what the other

actly

is

about to say and when, each can “react” to the

other without any delay for a signal to go from one to the other. idea that a specific, subtle kind of predestination can explain

other puzzles of

and

is

modern

physics has been developed by

described in his popular

book

Timers

The

EPR and

Huw

Price,

Arrow and Archimedes'

Points Unfortunately, Price has encountered considerable technical difficulties in trying to

develop a predestination theory that takes ac-

known

count of the way subatomic particles are

But the

real trouble

with the postulates of predestination and in-

stant everywhere-to-everywhere links erful

merely to explain

problem becomes:

to behave.^

is

that they are

much

too

pow-

EPR correlations. If such phenomena exist, the

How

does the universe implement such remark-

ably efficient prevention of apparent faster-than-light causal effects and faster-than-light

communication of information? Where does the cen-

Antony Valentini has attempted to develop a kind of hidden-variable theory in which the early universe did have general faster-than-light causal links, which died away sorship

come from?

Italian physicist

naturally, except at the microscopic level,

siderations, but his views have not

been brave enough tially,

the idea

is

to suggest

due

to

thermodynamic con-

won wide acceptance. Valentini has

an experiment to

test his ideas.

to use a powerful telescope to capture

Essen-

photons that

were emitted very early in the history of the universe, and subject them to a two-slit experiment.

tern will not be found.

would be prepared will

be found.

I

He

predicts that the usual interference pat-

applaud his courage, but

to bet a substantial

sum

that

I

(and

many others)

no such anomalies

*

Another variation on the predestination theme is John Cramer s transactional interpretation.X^ramer invites us to imagine a “retarded

The Old Testament / 73

wave” spreading backward

in

time from the point

at

which

a system

is

measured, for example, by the absorption of a photon in a spespot, and interfering with the forward wave which we normally

finally cific

think of as constituting or guiding the photon. You could think in terms of a sort of “negotiation” or transactional discussion between the past

and the future that decides whether, lives

or dies. But this

for example, Schro^inger’s cat

way of thinking has proved too cumbersome

to

gain widespread acceptance.

Conclusion: Whither? The work of Price, Valentini, and Cramer actually represents the respectable end of an endeavor that has become increasingly unrewardlifetime ago. ing, trying to cling to quantum interpretations invented a Other attempts have led even powerful ways.

I

intellects into

recently heard a rather distressing talk

Bohm’s

detailing

dubious path-

by a former colleague of

how his immediate circle at Birkbeck developed some

aspects of a cabal, complete with initiation

rites, as

an ever more

iso-

group attempted to explain away the contradictions of quantum with ideas borrowed from literary theory and even psychoanalysis. Bohm died, in the judgment of many who knew him, “badly bewitched

lated

by philosophy.” Philosophical discourse into quantum has taken some unhelpful turns, most especially with respect to the claim that asking certain questions about quantum systems is meaningless or forbidden. Because everything in the universe

an extension of this attitude could pretty tific

is

in fact a

much

quantum

spell the

system,

end of scien-

endeavor.

eschew philosophical excuses and outdated notions. We sense are looking for a physical, visualizable solution that our common can accept. Because none of the ideas above properly address the PPQs

We

will

we have formulated, we must look

for

newer ones.

V

CHAPTER 6

LET’S

ALL

MOVE

INTO HILBERT SPACE

t

which quantum mechanics has indisputably progressed since the interpretations discussed in Chapter 5 were invented. To understand it, we must prepare to visit a rather

here

T

is

one way

in

strange place that was invented by the mathematician David Hilbert. It is

called Hilbert space in his honor.

State The key idea

is

Space

that in a space with a sufficient

number of dimensions,

a single point can describe the state of an entire system,

We’ll start with a simple example. Let’s suppose

business that transports goods between

own just one

truck and

way between

the two

cities,

on

moment by

a point

Figure 6- la.

The truck

But

it is

however large.

you own

a trucking

New York and Chicago. If you

always somewhere on the interstate high-

you can

indicate

its

position at any given

a one-dimensional graph, a straight line, as in is

driven by Albert.

now let’s suppose

that your business expands to

two

vehicles,

with a second truck driven by Betty. You could indicate their positions using two different points on your original graph, by using two different markers. But you could also indicate their positions using a single

74

.

Lefs All

Move

into Hilbert Space

point on a two-dimensional graph, as

shown

/ 75

where the

in Figure 6- lb,

horizontal axis gives Albert’s position and the vertical axis Betty

you got

sition. If

a third vehicle

and

driver,

you would need

dimensional graph to keep track of the whole as in Figure 6-lc,

po-

a three-

fleet

with a single point,

will

need an n-dimen-

and so on. Obviously, you

You cannot readUy

sional graph to keep track of n trucks.

s

graph of more than three dimensions, of course, but

it

visualize a

perfectly

is

possible to handle mathematically.

you switch your business

If

to operating a fleet of ships,

you

will

need a graph with two dimensions for each ship, because ships are not confined to roads, and can freely roam a two-dimensional surface; it

two coordinates per ship

takes

to record the latitude

To know what orbit a spaceship

tude.

know

vehicle, to include the alti-

would need three coordinates per

Aircraft

not only

tions, so

it

its

position but also

going to follow, you need to

is

speed in the

its

and z

x, y,

direc-

takes a graph of six dimensions to record the full trajectory

information for one spaceship.

If

you have 10 spaceships, your graph

needs 60 dimensions, but a single point on

mation about your

Of

and longitude.

fleet that

you need

to

it still

records

all

the infor-

know.

course what we’re really interested in

is

not trucks or space-

ships but fundamental particles. If the universe consisted of pointlike classical particles,

we would need 6N dimensions

to keep track of a

N particles including their positions and speeds:

system of

12

dimen-

sions for a two-particle system, 18 for a three-particle system,

and

so on. There are perhaps 10^® particles in the observable universe, so a single point in a space of

about

10^^

dimensions could record the

exact state of the entire classical universe. wait.

.

If that

sounds

like a lot, just

.

Probability State

Quantum

Space

systems are more complex than classical ones and require

more information just

^

to describe

one truck, but

it’s

a

them. Suppose you are back to owning

quantum

one. Even

if it sticks

to the route

described not by a dot

between

New York and

on

but by some kind of probability wave having a specific value

a line

Chicago,

its

position

is

76

a

/ Schrodingers Rabbits

CH

NY Albert

'V

v>

CH

Betty

NY

CH

c

FIGURE

CH

Albert

6-1

Keeping track of

(a)

one truck,

(b)

two trucks,

(c) three trucks.

Move

Let's All

/ 77

into Hilbert Space

#

CH

NY Albert

FIGURE

at

6-2 Albert’s probability wave.

every point along the route, as

plies that Albert tends to loiter

This

is

bad news

shown

in Figure 6-2.

near the ends of his route.

our project to record

for

The shape im-

all

the information

about his position in the most compact way possible. To fully record the information in Figure 6-2, we would have to write down the height of the graph at every point along the x axis; an infinity of points, so an infinity of values. Things get more manageable if we only need to know

roughly where Albert

is:

say, in

which county out of 5 counties along

shown

in Figure 6-3a.

The

infor-

the route.

Then we

mation

given in the height of 5 individual bars, 5 numerical values,

is

get a bar chart as

and we could record

it

space of 5 dimensions.

graph might look

by placing If

we add

like that in

a dot at

an appropriate position in a

a second truck, driven

Figure 6-3b, and

by

Betty, her

we could record

the

position information for both trucks by a point in a 10-dimensional space. This

is

worse

—

in the sense

of more extravagant

ation for classical trucks or particles, but not that basic rule

twice as

is still

additive.

A two-particle system

many dimensions

to describe

it

—than the

situ-

much worse, for the

will require a space

of

as a one-particle system.

For display purposes, you could combine the information on both the graphs into a single 3-dimensional graph, as in Figure 6-3c. How-

s

78

FIGURE

/ Schrbdingers Rabbits

6-3a Probability of Albert being found in each location.

FIGURE

6-3b Probability of Betty being found in each location.

ever, at the

moment, Figure 6-3c does not contain any more informa-

tion than 6-3a plus 6-3b. Although

dimensional space generate

still

contains

it

all

has 25 columns, a point in 10the information

we need

to

it.

introduce Albert to Betty. The results are dramatic. all They start to interact; indeed, they fall in love and get married. It s wave devery sweet, but now the interaction makes the probability as shown in scribing where your trucks are much more complicated,

But

now

let’s

Figure 6-3d. For example, in

many

4

places the probability that Albert

Lefs All

FIGURE

Move

into Hilbert Space

/ 79

6-3c Joint graph of Albert and Betty before they meet.

Albert

FIGURE

6-3d Joint graph of Albert and Betty

after they start interacting.

80 / Schrodingers Rabbits %

and Betty

will

be close together

is

high, but for

some reason Albert

lives, when Betty is tends to avoid Cleveland, where his mother-in-law and Betty have started there. The point of the; story is that once Albert

to interact, the probability iVave describing

composed

into

two simple Figures

like

them can no longer be de-

6-3a and 6-3b: Figure 6-3d

much information. There are 25 independent colin a space of 25* dimensions to it would now require a point

simply contains too

umns, so

record the information.

The

general rule

is

that

when we

two

join

classical

systems and

we just add the number of dimensions of the must multitwo originals; but when we join two quantum systems, we The Hilbert space of a ply the number of dimensions of the originals. number containing even a few particles has a mind-boggling them

allow

to interact,

system

of dimensions.

a

What is the significance of Hilbert space? Hilbert space represents quantum system before it is measured. When we do a measurement,

by a single point the space will collapse to a specific state represented cell phones and discover (as when we ring Albert and Betty on their But before a measurement is made, we can grey mist whose think of Hilbert space as being filled with a kind of system each point corresponds to the probability that the

their actual positions).

density at

mist turns will collapse to that particular set of values. This highly amenable to mathematical analysis;

it

slops

out to be

around following

that govern the bevery simple rules, in fact even simpler than those number of dimenhavior of a real fluid like water. So, despite the large an isolated involved, the best way to calculate the evolution of

sions

quantum system

is

to use Hilbert space.

you understand the dilemma of mathematical physicists beautifully simple. dealing with quantum. The rules of quantum are

Now

But

all

except the simplest

quantum

tiny isolated systems such as the

processes

—

for example, those of

hydrogen atom

happen

in a space

becomes impossible computers now available, and to simulate them on the most powerful own minds. utterly hopeless to try to visualize them with our

of such a colossal

number of dimensions

that

it

Lefs All

Move

into Hilbert Space

A Space Hilbert space

is

of Her

/ 81

Own

usually described as totally abstract, utterly remote

from the three-dimensional world of our ordinary perceptions. But there

is

a

well-known experiment that

calls for

creating a^arge bubble

of Hilbert space, embedded within the everyday world, which you could in principle touch.

about Schrodinger

To

really

s

We have encountered it already. I am talking

famous

cat.

do Schrodinger’s famous

cat experiment,

we would need

box that no information could leak out of, a box of macroscopic size that was truly and utterly sealed from the outside world. Just for fun, let us see if we could conceivably do this with

to create a cat

present or near-future technology. In the interests of both scientific progress and cat welfare, server, a

we

will replace the cat

human

ob-

kind of philosopher-astronaut.

It is vital

that the

box does not touch anything, so we

going into space where

it

without any connecting

can be allowed to struts.

charged particles called cosmic space,

with a

we

by

microgravity

float free in

To shield against the high-energy

rays,

which

hollow out a chamber

will

will start

found everywhere

are

at the center

of

some

in

natural

an asteroid or comet nucleus. We must then protect the central chamber against particles caused by radioactive decay of elements in

object,

the asteroid, probably with a thick shield of pure metal. telling

you an odd

1940s,

all

the steel

fact at this point. Since the first

made on Earth has been

slightly

radioactive particles present in the atmosphere, into the blast furnace because large

bustion.

When

scientists

need

radioactive nuclei, they get

War

I,

the

German

it

land, the giant natural harbor

based.

When

from

atomic

contaminated with

which inevitably for

get

com-

completely free of decaying

was scuttled

is

resist

tests in the

a surprising source. After

where the

nonradioactive steel

cannot

amounts of air are needed

steel that is

battleship fleet

I

British

at

World

Scapa Flow in Scot-

Grand Fleet used to be

required, scuba divers go

down

and carve chunks of pre-Atomic-age steel from the battleships, which thankfully provide a huge resource of the material. Within the asteroid,

we will construct a thick sphere of this ultrapure steel. The cat box, or philosopher box as it is now, floats within

this

82

central shield,

/ Schrodingers Rabbits

and within

Christmas bauble that in the milli- or

is

it is

a further thin spherical shell like a

cooled to the lowest temperature practicable,

perhaps even micro-Kelvin range, to suppress the ra-

the inner shell contains a perfect vacuum emitthe very occasional very low energy infrared photon

diation of infrared photons,

except for

Because such photons have a wavelength of several the central meters, they reveal nothing about the position or state of

ted

by the

walls.

chamber beyond the

fact that

it is

In theory, the space capsule

there.

now no

longer contains a philoso-

phipher-astronaut, but a Hilbert space, a probability distribution of losopher-astronauts doing increasingly divergent things, as their

personal histories diverge depending on exactly

how many photons

quantum

events that multiply

hit

each

cell

of their retinas and other

we could look inimpossible), we might imag-

into macroscopic consequences in various ways. If side the capsule (which

is,

by

definition,

Is the ine seeing something like a multiple-exposure photograph. space? astronaut writing, or brushing her teeth, or just staring into

This

is

the image that inspired the

title

of this book. Rabbits are

fa-

tendency to multiply; what a Schrodinger box really contains is not one of what we originally put in it, but many. We have seemingly created a macroscopic bubble of Hilbert space,

mous

in

for their

which

eventually different probability histories of the astronaut,

principle, we diverging quite significantly, can trace themselves out. In could do a test to prove that this has happened, using interference

between the different

histories,

the last chapter. However,

and we

when

will return to this possibility in

the capsule

is

opened the astronaut

—the Hilbert space

herself will report nothing out of the ordinary

instantly collapse to a single point, selecting just states that

it

one of all the possible

has been exploring.

Alas, there

ment

will

is

at least

impossible, despite

we do not know how

one all

effect that

might

still

make

our elaborate precautions.

to shield against

is

gravity.

this experi-

One effect that

Although the center

matof the capsule will automatically remain in the same position no symmetrical obter how the astronaut moves about, only a perfectly

can have a perfectly' spherical gravitational field. it like Earth or a space capsule with an astronaut in object

ject

—

A

real

—has

a

Lefs All

field

Move

into Hilbert Space

/ 83

with subtle variations betraying information about the internal

disposition of

mass.

its

Remember

shifting a small rock light-years

which

tions of air molecules in Earth

thought experiment in

Borel’s

away could change the posi-

atmosphere, via gravitajional

s

amplified with every molecular collision?

It is

effects

difficult to calculate the

would continuously measure the capsule the above experiment, but it might well be sufficient to make the

extent to which such effects in

macroscopic superposition we are trying for impossible.

Natural Collapse The

analysis of Hilbert space has

on the process we

call

quantum

thrown an extraordinary new collapse. In 1970, Dieter

Zeh

light

at the

University of Heidelberg demonstrated something remarkable. In a

system that evolves in Hilbert space, whose components interact nificantly, the

mathematics predicts that although

appear to proceed quite unselectively

—there

what position one particular particle

is

ertheless start to

is

likely to

emerge that are durable

sig-

at first sight things

no telling, for example, occupy

—patterns nev-

in the sense that they con-

tinue to be strongly affected by patterns of high co-probability, but in a rapidly decreasing fashion

by patterns of low co-probability. The

mathematical process by which inconsistent patterns exert increasingly small effects on one another

Decoherence can

is

called decoherence.

effectively explain

quantum

apparent quantum collapse. To see how,

tem of Schrodinger’s

cats.

Assume

let

kill

—or

at least

us consider a nested sys-

that the astronaut described above

takes into the capsule with her a small cat lines,

collapse

box designed on the same

with Schrodinger’s original diabolical arrangement that might

the cat with 50 percent probability.

We

seal the capsule.

and the

cat are in Hilbert space.

she will open the box. It tells

states

point of view, both the astronaut

know that after a certain time, Hilbert space model now reveal?

But we

What does the

us that as soon as she starts to open the cat box, the possible

of herself very rapidly become entangled with those of the

There are states

From our

states

of her that are rejoicing, having found a

live cat,

cat.

and

of her that are mourning, having found a dead one. But these

84

/ Schrbdingers Rabbits

effect on one different states very rapidly cease to have a significant collapse in state of her has apparently seen a^quantum

another. Each

cat has

which the At

this

point

worlds because: sule?

You

become it is

definitely dead, or definitely alive.

What happens when you open

are going to see either a

her arms, or a sad

mention of many-

reall^ irhpossible to avoid a

woman

happy

the astronauts cap-

woman

holding a dead one.

If

with a living cat in

you accept

that the

what is really Hilbert space analysis applies to the whole universe, then the happening is that one version of you is becoming correlated with happy-live-cat outcome, and another version of

you with the sad-

dead-cat one.

We

will

have more to say about

yet claiming that this

is

this later,

but

I

a proof of many-worlds.

might describe the opening of a Schrodinger

s

cat

am

A

certainly not

single-worlder

box something

like

this;

“When I opened the box, the outside environment started to measure

what was

box might ton

at the

in there.

The very

give a strong clue

temperature of a

“Just as

when you

—

first

measurement photon out of the

for example, if

it

was an infrared pho-

live cat.

scratched one lottery card,

it

made

a certain

outcome of scratching the other more likely, so a measurement conmeasurements consissistent with (say) a living cat makes subsequent outcome more likely. And so either a live cat or a dead the abone emerges, rather than some gruesome combination. From measurements brought a stract processes of Hilbert space, consecutive

tent with that

specific consistent reality into being.”

The single-worlder might have count above,

it

a point. Despite

my simplified ac-

remains controversial whether you can in

fact get sen-

numbers out of Hilbert space without some form of context dependence some privileged starting point such as a unique reality from which you can measure everything. But we will postpone this argument to a later chapter, and concentrate for now on the solid

sible

—

achievements of decohereqce.

2

Let’s All

Move

into Hilbert Space

/ 85

Decoherence

Testing

Decoherence theory allows us to calculate exactly the timescale over which any given system will decohere in the old language, the time

—

quantum

for

but

it is

collapse to happen.

useful to get

some

take in certain situations.

idea

One

small objects whose position

which they

actions in cinity.

Table 6-1

The top ticle

left

is

scatter

am not going to descji^e the math, of how long collapse is predicted to I

sort involves the spatial localization of

is

measured from time to time by

photons and other particles

in their vi-

adapted from a paper by Erich Joos.^

figure in this table tells you, for example, that a par-

of dust a hundredth of a millimeter across (just big enough to be floating in interstellar

visible

with a strong magnifying glass) that

space,

and whose position has become uncertain by

likely to

pop

However, its

inter-

own

is

to a relatively precise location in

if its

position

is

a centimeter,

is

about a microsecond.

uncertain to only about the same distance as

diameter, a hundredth of a millimeter,

it

second or

will take a

so to get relocalized. Note the huge variation from the top right to the

bottom

left

of the table. Relocalization becomes

much

faster as

you

approach Earthlike conditions of temperature and atmospheric pressure. It also gets much faster for larger objects. There is probably no-

where

in the natural universe

where objects

larger than dust grains are

delocalized to any significant degree, because the

TABLE

6-1

famous

3® Kelvin

Localization Time (seconds-cm^)

a=

10-3

300 K photons Sunlight (on Earth) Laboratory vacuum

o=

10-3

cm

a=

10-3

Dust

Particle

Particle

10-*

W

10^2

10-”

10-'2

10-3

10-2'

10-^7

10-'3

10-23

10-”

10-'

10-36

10-32

10-30

(10^ particles/cm^)

molecules (standard atmosphere)

Air

cm

Large Molecule

Dust

Cosmic background radiation

cm

— 86 / Schrodingers Rabbits M

Bang, cosmic microwave background radiation, remnant of the Big

is

\

all-pervasive.

There are subtler forms of decoherence than simple localization,

whose however. Another system of intere^'is a regular oscillator tion

slowly decaying, like a swinging

is

pendulum

mo-

subject to friction.

is directly turns out that the decoherence time of such a system that is, the time it takes for the related to the damping time

It

—

link be pendulum’s swing to decrease to half its original value. This the tween quantum decoherence and the increase of classical entropy, important theo slowing of things due to friction, is a tremendously

Unfortunately for anyone hoping to witness a pendulum swing (an effect you can in a superposition of different angles of its time sometimes see in trick photographs), the ratio of the decoherence

retical result.

to the decay time

is

extremely small, of the order of

10"^®

in the case of

1-gram pendulum on Earth.

a

However,

this ratio

is

proportional to the absolute temperature of

the surroundings, and to the mass of the object. able for a small object spinning in a

damping time fects

is

It

gets

vacuum, an object

more for

reason-

which the

efalso extremely long, because there are only tiny

tending to slow the spin. Such an object can remain in a superpoagain, of different angular positions for an appreciable time, but

sition

in interstelnaturally occurring examples are spinning dust particles lar

space rather than large terrestrial objects.

Feasible Experiments Let us is

now return to

not just a theory.

and emphasize that decoherence in doable experiments. Such tests

Earth, however,

It

can be tested

Anton have already been performed by the redoubtable experimenter, experiments Zeilinger of the University of Vienna, with interference molecules using relatively large objects fullerenes, football-shaped whose basic form is a cage of 60 carbon atoms.

—

Zeilinger looked at ways in that

is,

which environmental decoherence

the environment “reading” the position of the molecules degrade the inteirference pattern obtained in a two-slit

tends to

experiment.

One such

test

involved doing the experiment

in*

a space

Lefs All Move into Hilbert Space / 87

that

was not

a perfect

vacuum, so

that occasional collisions with gas

molecules caused decoherence, degrading the interference pattern.

Another used molecules that were hot enough

to emit infrared

pho-

tons as they flew along their trajectories, giving away^ information

about their positions. In both experiments, the predictions of decoherence were con-

firmed.

The

error bars were relatively large, but

new experiments now

being proposed should dramatically increase the accuracy. Indeed, as we’ll see in a later chapter, devices like

quantum computers, which

are

extremely sensitive to the effects of decoherence, naturally provide a

way of measuring it to very high

accuracy,

and that

is

part of the moti-

vation for trying to build such devices.

Unless something very unexpected emerges, the mystery of where,

when, and how quantum collapse occurs must be considered solved. is,

quite simply, decoherence that does

it.

Dieter Zeh’s hypothesis has

been confirmed by 30 years of calculation and experiment, and

something of an indictment of the system by which is

Quest of the

advance is

not

Finite

There was one point about Hilbert space that fact that strictly speaking, the probability

exact value everywhere. If

infinities, let First,

me throw you

there

is

relativity that the

wave associated with even a

is

a lifeline

—

a

dimensions to describe

good

in fact,

physicist’s distaste for

two

lifelines.

nowadays strong evidence from the

field

of general

maximum amount of information that can be stored

and retrieved from

universe

you have

rather skated over; the

I

single particle needs a Hilbert space of infinite

in

it is

known.

In

its

scientific

recognized and popularized that this tremendous progress

better

It

a finite-volume region of our three-dimensional

itself finite.

There

the Bekenstein limit after

its

is

even a formula for calculating

discoverer.

No one knows

it,

called

yet quite

what

implications this has for Hilbert space descriptions of the universe.

There have always been awkward clashes between general

and quantum theory. But

it is

possible that

of dimensions required for Hilbert space

is

it

means

relativity

that the

not quite

number

infinite,

merely

88 / Schrodingers Rabbits \ %

mind-bogglingly colossal

(still

much larger than

the mere 10*' dimen-

classical universe). So, wherever I sions or so required to describe a with Hilbert space dimenhave used the word “infinite” in connection might be possibly substitute^Vast.” The implications

you can

sions,

important, but this

is

a very controversial area that

we will return

to in

the final chapter.

one aspect of most kinds of particles that mind-boggling number, of dimenrequires not an infinity, or even a two. As well as having Hilbert space to describe it, but exactly Be that

as

it

may, there

is

sions of

a position,

many

particles have a

called spin in the case of electrons tons. Spin

much

simpler intrinsic property,

and polarization

and polarization represent

in the case of pho-

internal properties of particles.

might represent something like In terms of our trucker analogy, they regret is currently pointing. (I the angle at which the driver’s cigarette chain-smokers.) that Albert and Betty are both to

tell

you

External

properties like position along the x axis

quantum

must

an infinity of real numbers, be represented by a waveform containing found at each possible point giving the probability of the particle being along the real

axis. After collapse,

number which

still

the result of a

measurement

is

requires an infinity of digits to record

a single its

exact

The universe “knows” an infinity of real polaryou one back. But a quantum value such as

value, like 119.3564218

numbers^ and gives

ization can be represented

tion in

which

by

just

Albert’s cigarette

is

compass bearing and elevation back just one

two

real

numbers—like

currently pointing, given

—and when you

collapse

the direc-

m terms of it,

answer, as if all single binary digit, a yes-or-no

record from outside the truck

is

you

get

you can

whether Albert ultimately discards

left-side window. the cigarette stub out the right- or The two real numbers describing spin could be

drawn rather

columns, but a neater unimaginatively in a bar-chart with only two called the Bloch sphere after its inventor. is shown in Figure 6-4,

way

Here the direction of the cigarette

is

pointing)

is

shown

on an imaginary sphere. the north or south pole. It

was David

particle’s spin axis (the direction Albert’s

as the latitude

and longitude of a point

On measurement, the vector shoots to either '

Bohm who

first

realized that, in a less-is-more kind

of way, using these modest internal

quantum

properties might yield

Let's All

the

most

practical

locality that

way

we met

Move

to

into Hilbert Space

perform the kind of

/ 89

test

of quantum non-

in the Bell-Aspect experiment, far

more doable

than the experiment originally proposed by Einstein. Later, David

Deutsch and others realized that harnessing these internal quantum

quantum computer. Before measurement, the uncollapsed vector shown in Figure 6-4 can be thought of as a qubit, the quantum equivalent of a binary digit; when it is collapsed

values

is

way to

also the

by measurement,

and

1

it

to the north

tum computers,

a viable

becomes an ordinary bit, by assigning the values 0

and south poles

in the diagram. For

more on quan-

see Chapter 11.

Not a Panacea The arena of Hilbert space, and the process of decoherence, have given us deep insights into

quantum

that the pioneers

interpretations did not have. But the selves

new

who

invented the old

concepts do not by them-

answer the key interpretational puzzles of our PPQs and they

do not help us

to visualize the processes of

space and time

we

story of what

going on.

is

are familiar with, to

quantum

tell

in

terms of the

ourselves a meaningful

90

/ Schrodingers Rabbits

real space conIndeed, the relationship between Hilbert space and troul^ling feature of quanceals rather than explains perhaps the most

tum,

nonlocality.fSometimes things that happen in a smooth, its fluidway in Hilbert space, as th^ gray shading develops

its

m

orderly

in ordinary way, can correspond to rather startling goings-on which arises because two space. We have already met the EPR paradox,

like

photons widely separated Hilbert space. There

is

in ordinary space

another quantum

apparently faster-than-light

rise to

can share the same small that can give

phenomenon

effects.

that you Most people have heard of quantum tunneling. Suppose electron at some kind of wall that fire a particle such as a photon or an to penetrate. The wall can be an actual it doesn’t have enough energy or a more subtle barrier, such as a thin sheet of aluminium,

physical

energy barrier, the equivalent of a sufficient

energy to

rules of quantum

roll

up and

mechanics

—

hill

over.

that the particle does not have

Under

these circumstances, the

specifically, the

Heisenberg uncertainty

associated with principle— predict that because the probability wave

the particle slops over

beyond the

wall, occasionally the particle will

be an imappear to tunnel straight through what would otherwise its probjust by happening to jump from one part of passable obstacle, ability

A

wave

to another.

disturbing feature of

happen

instantly.

across

Those are

that

it

appears to

can describe this in words: “Any time that you of the particle, you will find that it is on one side

The implication is that the wall in no time at all.

the wall or the other.

moved

is

We

choose to measure

have

quantum tunneling

just words.

at

some

point,

it

must

But the mathematics does also seem to de-

instantly, scribe the particle leaping across the wall

and when you

computer simulation of the probability wave associated with the particle is most likely the particle, the central part describing where does indeed seem to proceed faster than light. The mat-

watch

a

to be detected ter is unclear

enough

that experimental physicists, including highly

can transmit data respected ones, have run tests to see whether they even claim to light using quantum tunneling, and some faster

than

have succeeded.

'

Lefs All

Now, before anyone most

certainly can’t

do

Move

into Hilbert Space

gets too excited, this.

More

I

/ 91

hasten to add that you

careful work, both in

al-

computer

simulations and with actual photons, indicates that although the probability

waves do seem to

travel faster

than light

cannot propagate a disturbance along them really

send information

imply.

faster

than

light,

at certain points,

at this

you

speed. ifou cannot

with the paradoxes that could

My point is that a good visualization or interpretation of quan-

tum should not even tempt Hilbert space

is

a

good place

us to think such a thing could happen. to

do math, but

with a clear intuitive picture of what sional world.

is

it

does not provide us

going on in the three-dimen-

V

CHAPTER

7

%

PICK-YOUR

OWN

UNIVERSE

v-»

both good news and a warning. The good correct news is that there will certainly be more than one fully way to look at quantum. In a sense, we have an infinity of choices.

his chapter contains

T

The warning

is

that

it is

perilously easy to

progress rather than helping

cautionary

it,

and we

a choice that hinders

make

shall

look

at

some pertinent

tales.

N

A Choice

of

Gomes

actuan ancient idea that events here on Earth are merely the It appears in Greek alization of a game being played between gods.

There

is

legends, in the Norse sagas of the Vikings, tures

all

of gods

and

in folk tales

around the world. Most people no longer believe

who

can control

the past century the

ard Feynman.

We

human

beings like pieces

metaphor was revived by the

on

from

in a

cul-

panoply

a board, but in

great physicist Rich-

He wrote:

which can imagine that the complicated array of moving things played “the world” is sojnething like a great chess game being

constitutes

know what the by the gods, and we are observers of the game. We do not watch the playing. Of rules of the game are; all we are allowed to do is to

92

Pick Your

Own

Universe

/ 93

we watch long enough, we may eventually catch on to a few of rules. The rules of the game are what we mean by fundamental physics.

course, the

if

As usual with Feynman’s

insights, this

opens up a rich vein of

thought, going far beyond the immediate purpose for which he used

One such development

the metaphor.

when

it

comes

Many

is

remarkably efnpowering

quantum physics. have heard of game theory,

to interpreting

readers will

a field of

math-

ematics whose applications include finding optimal strategies in such fields as business, military conflict,

sions of others

games

theory,

and bridge

—

deci-

must be taken into account. Rather more obscure

which concerns

usually

accessories. Yet

and deterrence, where the with

itself

real-life

games involving boards,

games

games such

cards, dice,

is

as chess

and suchlike

theory, too, has practical applications. For ex-

ample, a lateral-thinking approach to proving a mathematical theo-

rem

Imagine a game played between two mathematicians: A,

is this.

who wants

to prove the theorem,

and

B,

who wants

can prove that A has a guaranteed winning the theorem all

is

the various

proved, without needing to

moves

An important tion

A and

insight

on which the whole

to refute

strategy^ for the

work through

trivial

example

is

If

we

game, then

the details of

B can make.

—indeed, the founda-

from games theory

field is

based

—

is

the fact that

many games

that appear quite different are, in fact, algorithmically the

A

it.

the different editions of the

same game.

game Monopoly

that

are played in different countries. In each country the properties are

labeled after districts of a great

most expensive property

city.

Thus

in the

American

edition, the

called Boardwalk; in the English,

is

Mayfair, once London’s most fashionable area; in the French,

Rue de

same

in

la Paix.

it

it is

is

the

But the rents and prices of the property remain the

each case, so of course this relabeling makes no difference to

the game.

Nor does

the fact that in the English version the prices are

nominally in pounds, and the French in euros. In the old French version the prices were in francs, francs, the numerical prices

spect to the

currency

American

bills

and

and because

were

version.

it is

is

worth about 10

multiplied by exactly 10 with re-

The addition of an

prices likewise

In the case of Monopoly,

all

a dollar

had no

effect

extra zero to

on the

all

the

play.

not hard for adults to distinguish the

94

/ Schrqdingers Rabbits X

game from

algorithmic part of the get a card informing

you

that

the story component.

you have won

When you

a beauty contest, or that

it

course how many your birthday, the significant information is of whose account to whose. points (money) are^ to be tYansferfed from A few years ago, on a But children can have difficulty even at this level. next to a charming lady long airplane flight, I found myself sitting

is

whose son was happily occupied with

a

book on

the

game Pokemon,

among preteens. I chatted with the mother and game separated the world sharply by age group.

then a worldwide fad

we agreed

that the

even those Whereas children were obsessed with it, almost no adults the basic who were parents of young children—had any idea of even overheard our conversation, rules or objective of the game. The kid amusing but unand decided that it was his duty to educate us, with how the game productive results. He was trying his best to describe

worked, but could think of no other way to preamble, telling us

how

the

Pokemon

start

than with the story

characters (represented by

bottles on a special belt. cards) were mouse-sized creatures carried in apWhen it came to the cards themselves, realizing that a grown-up

proach was called

for,

he skipped embarrassedly past childish-looking

found something that fit the bill. You 11 like this Green Brain-Blaster, it’s really one,” he said proudly. ‘Tfs the Great

creatures until he

.”

good.

.

.

of the game, he Desperate though he was to describe the essence abstraction: “What found it impossible to reach the required level of really matters

is

the points

number on each corner of

the card.

You .”

then subtract. add the ones in the top left-hand corners together, adults, too, can find Before we laugh too hard, we should reflect that harder than it seems. the distinction between story and essence .

Let us

embark on

a field trip.

The

idea

is

simple: to find

.

some gods

them for a while, and figure out what the game is. A couple of thousand years ago, we would have climbed Mount Olympus playing a game, observe

but

this

discover

We

being the 21st century,

we

will fly off in a spaceship until

we

7-1.

some promising-lqpking gods, as shown in Figure playing might realize that the game these alien gods are

in fact

Pick Your

Own

Universe

/ 95

#

FIGURE nation.

7-1

These

aliens are playing a

game

By patient observation we discover

that involves speaking

that nine different

words

words

in alter-

are used,

and

of once per game. The players take turns to utter a word until the last one to speak wins. Games are a minimum of five and a maximum of nine words long (because all the permissible syllables have then been used). Nine-

each

is

used a

syllable

maximum

games sometimes end

shorter ones never do. syllables

We

in a

draw with neither player winning, although

see that the rules are consistent. If a given sequence of

wins on one occasion,

it

does so on any subsequent occasion.

it

in their heads,

we

learn the rules

be quite simple, but unfortunately they are playing

without use of board or counters. Yet because in due course

and beat them.

We

we want

might

start

to

it is

vital that

be able to play against these gods

by tabulating

games, as shown in Table 7-1, in which the

all

first

the different possible player’s

moves

are in

96

TABLE

7-1

List

of

All

/ Schrodingers Rabbits

Possible

Gomes god

1

wins

XIG flump WIBBLE nio%AG choo

god

1

wins

XIG flump WIBBLE

god

1

wins

god

1

wins

XIG flump WIBBLE nias

AG choo GAH

^

DOH gah FIZZ nias AG choo D(5H fizz GAH

XIG flump WIBBLE nias

AG choo

FIZZ

%

XIG flump WIBBLE nias

AG gah CHOO fizz DOH

drawn

XIG flump WIBBLE nias

GAH ag DOH choo

god

.

.

.

and

2 wins

so on.

and the second’s in lowercase. Unfortunately the table will be entries, that is, rather long; it could have up to nine-factorial 9x8x7x6x5x4x3x2xl = 362,880. In practice it will be less than that, been played, because many games end before a full nine moves have

capitals

but

we

will

As an ‘aid

still

be looking

to playing the

at a

game

book

—

the size of a telephone directory.

telling us

what move to make next

against a to have the best chance of winning, even

ing god

—

it

will

be pretty

much

useless, at least

randomly

play-

without the aid of a

computer. Fortunately, patterns in the data soon all

often wins

useful; wibble, fizz, gah,

you work out the

and

flump, wibble

ni, ag,

choo

gah, doh, fizz xig, ni,

gah

flump, ag, doh wibble, choo, fizz xig, ag, fizz

wibble ag, gah

zig

come somewhere

secret: there are eight

namely,

xig,

ex-

ag the words appear equally potent. Whichever god says so that game. Flump, choo, nis, and doh are not nearly

ample, not

ally

become apparent. For

%

“magic

in between. Eventutriples”

of syllables,

Pick Your

Own

/ 97

Universe

The first god to include a complete magic triple in the words it has spoken it does not matter in what order the words of the triple are wins. This is called, or whether it says other words in between them in a sense a complete description of the game, and it is certainly more

—

—

compact than the telephone-directory-length Moreover, because the tries,

list

of all pdsirible games.

of winning strings exhibits certain

symme-

the expedition’s mathematician could find ways to code the in-

formation

still

more compactly. But you

still

going on in the gods’ heads as they play, and will

list

win when the time comes

one of them

for

you

have no

little

feel for

what

is

confidence that you

to leave the ship

and challenge

yourself.

Then the expedition’s physicist comes to you. “I have it!” he shouts triumphantly. “The aliens are playing a simple game with sticks. Here is

my interpretation. “They

1

start

with an imaginary pile of nine sticks measuring from

unit to 9 units in length. Each alien claims a stick from the pile by

calling

tem.”

its

length.

I

have cracked the code for the alien number sys-

He writes down

flump =

the following table:

1

gah = 2

choo =

3

=4 ag = 5 xig = 6 ni = 7 fizz

wibble = 8

doh = 9 “Each alien takes a tion, until

he has a

set

stick in turn,

adding

from which three

it

to his personal collec-

sticks

add up

to exactly 15

me remind you of the first game we saw, the game that went: XIG flump WIBBLE ni AG choo DOH gah. After those moves, the first alien has chosen sticks of length 6, 8, 5, and 9 units. No units in length. Let

three of these add to 15.

and 2

units.

No

The second

three of these

add

alien has sticks of length

1, 7, 3,

to 15, either. But then the first alien

V *

«

98

says

/ Schrodingers Rabbits

FIZZ and claims the 4-stick. Now 6 plus

duly wins.

I

5 plus 4 equals 15,

and he

have solved the mystery; the aliens ^are playing the one-

dimensional game Fill-the-Gap.”

You bursts

are in the

middle 'of congiatulating him when the cabin boy

in.

“Captain,

I

have solved

it,”

simple two-dimensional game! position system.”

“Really,

He shows you

sir, all

he shouts. “The aliens are playing a I

have cracked the code for the alien

the following table:

xig

flump

wibble

ni

ag

choo

gah

doh

fizz

the aliens are doing

is

playing tick-tack-toe. Re-

member the first game we saw, the game that went XIG flump WIBBLE ni

AG

where

choo

DOH

gah? After those moves the board looks like

the' first alien writes

X and the second O:

X

o

X

o

X

o

o

X

this,

Pick Your

“So

far,

Own

Universe

/ 99

neither alien has a line of three. But then the

first

alien

‘FIZZ’ and wins with a diagonal line.”

calls

scratch your head, completely baffled. Both of

You

have an equally strong case. To

whom

you going

are

them seem

to

to give the bottle

of whiskey you have promised as a prize? Are the aliens r^alJy playing a

one-dimensional or a two-dimensional game?

As you ponder the matter, there comes a knock

at the

door:

It is

the expedition’s archaeologist.

think

“I

stone,

I

can help,” he

says. “I

remembered the famous Rosetta

which carried the same message

in three languages.

It

inspired

me to draw a tick-tack-toe board labeled as follows.”

6

1

8

xig

flump

wibble

7

5

3

ni

ag

choo

2

9

4

gah

doh

fizz

“Why, of course,” you exclaim, “it

is

the

famous magic square: one

whose every row, column, and diagonal add to 15. With this board, you can see instantly how the numerical and tick-tack-toe interpretations of the alien game are really one and the same thing. It was obvious that

The

this

had

be possible, when you think about

it!”

archaeologist departs rather hurt, but your problem of

wins the prize

The

to

physicist

who

call a

meeting of the entire crew.

and the cabin boy present

their respective interpreta-

is

not solved. So you

tions to general applause. But then the expedition’s anthropologist

stands up. “I

have a better interpretation,” he

says.

“These aliens are gods

who would never bother with anything as trivial as tick-tack-toe. WBat matters to gods

is

worshippers. These gods are obviously picking sa-

/ Schrodingers Rabbits

100

V

male, cred triads of worshippers from a species that has three sexes, They female, and neuterj and three hair colors, black, blonde, and red.

names^of a group of nine people who between them

are calling the

possess every combmationx)f thesekcharacteristics. “It follows

from universal

triad of worshippers

who

aesthetic laws that a

god would want

a

are either as alike as possible, or as different

but who must have

as possible. Either three people all of the

same

different hair colors; or three people

with the same hair color, but

who must be of different sex;

or, at

all

sex,

the opposite extreme, three people

each of different sex and different hair color than the others. A group of the latter type must, however, include ag. I can tell from universal psycholinguistic principles that xig, flump, and wibble are male; ni, ag, female; and gah, do, and fizz neuter. Xig, ni, and gah are

and choo

doh redheads; and wibble, choo, and fizz darkuniquely important because her fiery hair and femininity

blondes; flump, ag, and

Ag is

haired.

symbolize the importance of contrast.

I

can also

tell

from universal

aesthetic principles that the gods are imagining their worshippers a in a vestibule lined with red velvet, and choo is wearing

gathering

bronze amulet.” Before you can

you

to

it.

He

is

“You are cannot All

this,

someone stands up and

all

talking ze rubbish!” he says in a French accent.

know what

is

are doing eez projecting

your

own

what game

zese aliens are playing

as well

choose any

story.”

You can sympathize with

is

cultural prejudices. Trying a futile exercise!

his sentiments

anthropologist’s absurdly rococo tale with

tions?

But surely he

Then

it

is

“You

going on in ze minds of zese alien gods.

to find

detail.

beats

the expedition’s cultural relativist.

po'ssibly

you

comment on

its

when

it

You might

comes

to the

wealth of unverifiable

being a bit hard on the other two interpreta-

occurs to you that they are, indeed, also colored by cul-

tural subjectivity.

The

fact that the

cabin boy used X’s and O’s as

symbols on the tick-tack-toe board was certainly culturally determined; and you need two kinds of symbols or objects that are easily distinguishable from one aribther to play tick-tack-toe sensibly, what-

you make. Even the adds-to-15 system was culturally influenced. Why choose positive integers from 1 to 9? You could number

ever choice

Pick Your

the squares instead from 0 to

Own

/ 101

Universe

then each line would add to

8;

12.

Or you

number the squares from -4 to +4, so that each line adds to zero. And why choose consecutive integers at all ... ? The only way to

could

avoid spurious cultural overtones

is

to stick to the aridity of the

mathematician’s minimalist algorithm, and not attempf't*^ visualize. Certainly, the cultural relativist will do,

is

mistaken to claim that any story

because stories contain statements that can be

as ones that cannot.

falsified as well

The anthropologist might have gone a bit over the

top about the red velvet, but the eight winning triads described by his

theory are the correct ones. There might be

many

correct tales to

choose from, but there are even more incorrect ones; for example, any tale that predicted xig, choo, and doh were a winning triad would be

wrong. But

it still

looks as

you

if

will

have to

the bottle of whiskey

split

not merely three ways, but potentially infinite ways, because games theory tells you that there

can be invented. Then

You want

it

is

no end to the supply of correct games

occurs to you that there

to go out there

and kick some

yourself without the help of a computer.

is

a point to

that

all this.

alien ass, preferably

all

by

From that point of view, there

no question which interpretation of those you have seen is the winner. Human beings have evolved to be extremely good at processing

is

two-dimensional patterns

—and

relatively

weak

should be your choice of

stract logic. In this instance, tick-tack-toe

arena.

It is

the cabin

boy who should

get the whiskey.

In the world of real physics, of course,

two-player solitaire,

game

we

are not dealing with a

like tick-tack-toe. Real physics

is

more

seeing what cards turn up. But an immensely

insight follows

and ab-

at arithmetic

like

empowering

from our study of games: There are bound

equally valid ways to look at the universe.

We

playing

to

be

many

are thus free to pick

whichever one we find most comfortable and useful to work with.

Note that I have not claimed

—although many have—

that the cur-

rent interpretations of quantum theory are as equivalent as the superficially different

forms of tick-tack-toe above. The question of whether

they are experimentally distinguishable the later chapters.

The point

experimental discoveries there

I

is

one that we

am making

may be, we

is

will address in

that whatever further

will always

have a choice of

102

/ Schrbdingers Rabbits K

ways to visualize the universe.

It is

our duty to our successors, to those

out and battle the laws of physics on territory beyond that currently explored, to make that choice the best one we can at

who must go

"

every stage. It is

most no

limit to the

universe. But there

bad

also twist a to

make

know that with sufficient ingenuity, there is alnumber of stories we can use to describe the

wonderful to

a

is

story,

one that

irrefutable.

it

from the history of proved theories, but

downside to such ingenuity.

We will

science. I

will

is

Its

application can

not a good way to look

look

at

at things, so as

two great cautionary examples

Both are now generally described

as dis-

argue that they are merely inept interpreta-

They cannot be proved wrong and it is only too plausible that if their proponents had been a little more ingenious, they might still be and our understanding of physics would be imaccepted wisdom

tions.

—

measurably poorer.

Cautionary Tale The

first

of these old interpretations

sometimes an

1:

Phlogiston is

the concept of phlogiston,

also referred to as calistogen. Phlogiston

invisible substance that

uids and gases.

It

permeated

all

solids

was postulated

—and indeed

conferred the property of heat; the

as

all liq-

more phlogiston

an object contained, the hotter it was. To phlogiston, all substances were porous, so that whenever you put a hot object in contact with a cold one, phlogiston flowed naturally from the hot to the cold until both had the same temperature, just like water flowing to equalize its level or gas to equalize its pressure.

Before the age of machinery, phlogiston really worked very well as an explanation of heat. Different substances differed in the amount of phlogiston they could contain per unit volume. In modern terms, we

would say fered in

that they have different specific heats. Substances also dif-

how

readily phlogiston could flow through them; in

modern

terms, they have different thermal conductivities. That was natural

enough; different substances also have different capacities to absorb and permit the flow of ordinary liquids through them (contrast what

happens when

a sponge, a 'book,

and

a house brick are placed in a

Pick Your

Own

Universe

/ 103

bucket of water). Phlogiston was compi'essible, but

it

possessed

some

kind of volume, because substances expand when they are heated. Inand to early destructible phlogiston explains why heat is conserved

—

scientists,

it

did seem to be conserved, because devices for turning heat

into mechanical

work functioned

One problem

at

extremely low efficiencies.

with phlogiston was that

any detectable weight. But a

more

far

serious difficulty

ent with the start of the industrial age ability

of machines to create

if

the shaft

is

heat can flow along

made of an it.

—and

that

became appar-

was the apparent

new phlogiston. A turning

erate unlimited heat at a point

even

did not appear to have

it

by means of

friction,

shaft can gen-

and

insulating material so that

this

works

little

or no

This simple fact was the downfall of the concept

of phlogiston.

How

lucky that

losophers of physics.

its

If

defenders were not as clever as

modern

phi-

they were, they could have easily explained the

apparent problem away. Because, of course, the shaft must have some device at the other end to turn it; for example, a steam turbine takes

steam in

at a

high temperature and ejects

of the device, heat

is

it

at a

lower one. At that end

consumed and phlogiston

is

apparently vanish-

The process could be explained by the hypothesis of phlogiston tunneling ^assuming that phlogiston just undetectably and instantly ing.

—

jumps from one place to another. Does this remind you of something? Nowadays, we can even weight. Einstein’s famous

in a sense verify that phlogiston has

E = m(3 equation

mass, and this includes heat energy. cal objects,

If

predicts that energy has

you take two otherwise

identi-

each containing exactly the same number of atoms, the hot

object does in fact weigh slightly

more than

the cold one.

The

differ-

ence was simply too small for 19th-century instruments to measure. We arguably had a very near miss with getting stuck with the notion of phlogiston, and failing to progress to the

more

general concept of en-

ergy.

Cautionary Tale A

2:

second famous example of a flawed

Epicycles

scientific

paradigm

is

tion of epicycles. Ancient astronomers, trying to figure out the

the no-

motion

104

/ Schrodingers Rabbits V

of the planets in the heavens, were handicapped by not one, but two, false

assumptions. The

center of the motion.

The second was

heavenly objects, must did not

move

was that Earth was

first

stationary at the

itself

that the planets, being perfect

in cir(Jes. Because the planets obviously

move

in simple circles, their

For each planet, an invisible pivot point did

epicycles. fect circle,

and the planet moved (on an

point in a second smaller

circle.

in

terms of

move

in a per-

motion was described

arm) about the pivot

invisible

This idea could crudely approximate

the motions of the actual planets as seen in the sky, but for greater

accuracy

it

was necessary to postulate second,

third,

and even fourth

epicycles.

Then came Copernicus,

new

the

Galileo,

hypothesis, that the

and

Kepler.

Sun was the

As everyone knows,

true center of the system,

with the other planets including Earth orbiting around the old assumption. epicycles

planets

What

not so well appreciated

is

need not have died

do not

do not move

orbit the

at

Sun, and slower

at that point.

constant speed, but faster

when they

planet’s nearest

and

that the direction of the epicycle

will

indeed

move and

are nearer the

farthest distances is

retrograde

fastest at its closest

If

motion

we assume

that

equal to the difference

is

—

from the Sun, and

that

motion of the main arm

slowly as the distance increases. for accuracy,

and they

are farther away. But this kind of

each planet has an epicycle whose diameter

direction opposite to the

that the idea of

is

Kepler discovered that the

can be explained quite well in terms of epicycles.

between the

displaced

in perfect circles, but in ellipses;

Sun

when they

it,

is, it

turns in the

—then the planet

approach to the Sun, and more

We are lucky that Kepler was a stickler

rejected this tempting fudge.

modern mathematical techniques and computers. Because we now know that just as

How fortunate

it is

that he did not have access to

a technique called Fourier analysis can approximate a

sional graph as a

sum

of an infinite series of sine waves (a technique

and engineering), so any threecan be approximated elliptical orbits

often used in applied mathematics

dimensional motion to

— not

just

any desired degree of acctiracy

circular motions.

two-dimen-

as the

—

sum

of an infinite series of

A sufficiently clever mathematician could even work

out a formula for predicting the epicycles of an object,

like a

comet or

Pick Your

spacecraft, entering

Own

Universe

our solar system

fo'r

/ 105

the

first

time. If the math-

ematics of Kepler’s day had been advanced enough,

we might have

been stuck with the concept of epicycles. This would have produced an odd puzzle covered, because in star, for

some circumstances

when

relativity

was

dis-

(planets orbithi^ a neutron

example), the imaginary pivot points of the epicycles could

perfectly well be

moving

faster

than

light. Scientists

would struggle

to

them moved faster fortunately always seemed to

explain how, although the invisible arms propelling

than

light,

the motions of the epicycles

cancel at the right

speed

moments, so

that the actual planets never broke the

limit.

Do

epicycles

remind you

at all

of the imaginary waves of

quantum? But enough of the negative. Before we pick our favorite story of

quantum, let us look at the approaches that have worked well oping the other aspects of the

scientific

world-picture

in devel-

we accept today.

—

V

N

CVlAPTER 8 %

A DESIRABLE LOCALITY %

t e have a choice of stories to ourselves about quantum, a \m choice of arenas in which to play physics against the gods. W But what gives us an expectation that a straightforward acV

V

tell

^

count

is

possible? Surely physicists, of all people, have of necessity long

been accustomed to accepting esoteric and unlikely Well, actually, no. For at least 2,000 years, right

stories?

up

until

quantum

came along, science had progressed by taking exactly the opposite attitude that the universe should be understandable, and that we could

—

find straightforward ways to visualize

what

is

going on. Nay-sayers is

no

reason the universe needs be comprehensible even in principle,

let

those philosophers

who

pointed out, rightly enough, that there

alone by our limited minds

And though

the approach

it

—were

cheerfully ignored.

worked spectacularly

well. Blindly optimistic

was, the expectation that the universe should conform to

simple principles that were not only understandable, but even aes-

our ape-evolved brains, yielded breakthrough after breakthrough. So the frustration many physicists now feel about being unable to understand quantum is not the mild disappointment

thetically pleasing to

of a gambler whose ticket has failed to win the rage of a player

who

sees his

lottery. It is the fierce

winning numbers come up one

106

after

A

—then

another

gets

Desirable Locality

home

/ 107

only to discover that Schrodinger’s cat ate

his lottery ticket.

However, the statement ern physics

about

is

that,

easy to accept needs a

scientific progress that

In the

without quantum, the

good old days

—

little justify^ing.

goes something like

say,

around

Isaac

rest

There

of

mod-

a

myth

is

this:

Newton’s time

—the laws

of physics conformed to reasonable intuition. All objects, from

moved and

liard balls to planets,

bil-

interacted in a logical fashion in a

universe that was easy to visualize. But then special relativity was in-

We

vented.

had

to accept that basic intuitions

about space and time

hard-wired into our brains were wrong. General ters

worse

standings,

still.

it

When quantum

theory joined the trio

merely underscored the lesson: The universe can be

understood only in terms of highly abstract concepts.

and we’re out

strikes

we can visualize. This myth is

—

it,

three

can only get worse from here on.

It

totally misleading. In

intuitive picture that

quantum

Let’s face

back to a simple world-picture

we’ll never get

development of special and general

leaves

made matof new under-

relativity

some very important ways, the

relativity actually restored a

simple

had been wobbling ever since Newton. And

sticking out like a sore

that

thumb.

However, there are several aspects of modern physics that are admittedly a little startling at first encounter. So before trying for an intuitive picture of the universe that includes

us

perform

first

weirdness, can

a

we

limbering-up exercise.

visualize the

relativistic aspects? In

following distinction: look as

if it is

what Is

its

If

world without

quantum

we overlook quantum difficulty,

follows, please keep a careful

the world behaving weirdly?

behaving weirdly, as we see

it

aspects, let

including

its

watch for the

Or does

it

just

from unaccustomed per-

spectives?

Hello, As we go from newborn babe

to adult,

successive approximations. Later, stages were, so

We

are

we

World

it is

our worldview gets refined by

easy to forget

will take things right

from the

how hard the early

start.

born with the laws of physics already programmed into

J05

/ Schrbdingers Rabbits N

*N

at least after a fashion.

our brains,

nious technique called the gaze chologist Karen

We know this

test,

invented by developmental psyask a day-old baby what

Wynn. You cannot

moment

thinking. But babies, almost from the

world about them.

osity at the

If

because of an inge-

it

is

of birth, gaze in curi-

something happens

in front of

them,

they normally watch as events unfold, then look away. However,

if

something occurs that the baby finds surprising, it stares for a much longer time. These “gaze time” measurements are quite objective and can be recorded on videotape for

thought processes are

later checking, so these

data on baby

much more reliable than investigations that rely

on anecdote, or on the mother’s interpretation of early-stage baby talk. For example, suppose an experimenter places three apples on a tray,

then lowers a curtain that blocks the baby’s view of

(empty-handed) experimenter approaches the tray and with the contents, then withdraws, and are

still

three apples

on the

glances briefly at them,

But

if.

And

there are

now two

fiddles

its

The

about

raises the curtain again. If there

the baby

tray, albeit in different positions,

and then

it.

attention wanders to other things.

apples, or four, the

baby

stares.

And

stares.

stares.

Similar simple conjuring tricks establish that babies have a whole set

of built-in expectations about the world. For example, they differ-

entiate

between the animate and the inanimate. Using

not yet wholly

clear,

they place the things they see into either the class

of the animate (objects that have the power to things they

come into

jects that are inert).

ished

when

move themselves and

contact with), or the class of the inanimate (ob-

Thus, a baby

a sleeping cat

is

mildly interested but not aston-

wakes up and walks away, or when a

pushes a building block across a table with her ing block starts

criteria that are

moving apparently of its own

finger.

But

if

human

the build-

accord, the baby gazes in

wonder.

These the

tests

first test is

distinguish

prove more than

is

at first sight

apparent. For example,

used to establish that babies have the innate ability to

numbers up

to

about

four.

But

it

also demonstrates that

babies start with a built-in ^pectation of conservation laws

or other objects, do not simply

pop

in

and out of

—

existence.

apples,

Nor can

they be teleported; otherwise, any missing or extra apples could sim-

A

Desirable Locality

ply have been transmitted to or from sight.

An

object

progression.

is

expected to

/

109

Somewhere out of the baby’s

move only by means of

a

continuous

am tempted to say that even a day-old baby knows that

(I

the science of Star Trek

nonsense.) Likewise, the

is

test

with the build-

ing block proves not just that a baby distinguishes between animate

and inanimate, but more subtly that

it

expects objects to affect one

another only when they are in physical contact. prised

when

a block

A key concept cally,

rather than

Indeed,

if it

is

moves

jumping around

in space,

is

baby

is

touching

locality.

Objects

and they

not surit.

move

lo-

interact locally.

how a baby could make comprehending the physical world. Of course a baby’s

in

brain does not have

all

preprogrammed

it

as a

somebody’s finger

already emerging here:

were otherwise,

any progress

if

A

into

it is

difficult to see

the information

—

far

from

it.

The

it

needs about the world

built-in expectations serve

kind of bootstrap, an outline framework of rules that will be

re-

peatedly refined and modified. For example, a baby has a built-in ex-

pectation that objects, including

itself, will fall

supported by other objects. Yet in due course, balloons,

and

it

aircraft as exceptions to the rule.

unless they are

learns to accept birds,

This progress, modify-

we go along, continues for quite some time. As we grow up, the data we get from personal experimentation, such as pushing our ideas as

ing our toys about, are increasingly supplemented by information

taught to us by others. The next section roughly charts the stages by

which the worldview of

a

modern

child progresses. Just as the devel-

opment of the human embryo approximately recapitulates our tionary history

—

for example, at

one stage

it

has

gills

—so the

evoluchild’s

conceptual progress approximately reprises the historical stages by

which

understanding has progressed.

scientific

Worldviews, Infant to Adult Nursery Physics

The world Sun, ible

is

a

flat

Moon, and dome. An

and stationary surface

stars are

that goes

on

forever.

The

high up above, stuck on some kind of invis-

invisible force pulls everything in the

same downward

110

direction,

making any

/ Schrodingers Rabbits

object

fall

unless

it is

supported by something

Inanimate objects stop moving as soon as you stop pushing them. Objects have definite |)ositions. Objects can affect one another only if

else.

they are touching.

"

%

Elementary School Physics The world are.

The

round. Gravity pulls you toward the center wherever you

is

Earth, Sun,

Moon, and

countless stars

all

hang

space of three dimensions, with the Earth turning as

it

floating in a

goes round the

some force, positions. Time is

Sun. Objects keep moving in the same direction unless friction, stops

such as

marked by

clocks,

sometimes

affect

them. Objects have definite

and events happen

at definite times.

one another without touching,

Objects can

for example,

by magnetism, or by light or radio waves encountered as different phenomena.

trostatic forces, all

—

by

elec-

these are

High School Physics As well

as physical matter, space contains invisible spread-out entities

around

itself.

electric charges (such as the current in a wire) create

mag-

called fields.

Moving

An

electric charge creates

an

electric field

netic fields. Accelerating electric charges (such as the alternating cur-

rent in a radio antenna) generate waves electric

and magnetic

made up of

fields that travel at the

rapidly varying

speed of light.

Electricity,

magnetism, and electromagnetic waves are merely different aspects of the

same phenomenon.

College Physics There

is

no such thing

as absolute rest.

the distance between two stars,

Measures of distance, such

and times, such

as

as the time lapse be-

tween two events, depend on the motion of the observer. Time can pass at different relative

space-time

is

warped by

raters

for different observers.

gravitation.

such as a planet orbiting a

Any

The

structure of

object falling under gravity,

star, is actually traveling in a straight line

A relative to the region

of space immediately surrounding

any one observer

less,

tions,

and

all

Desirable Locality /ill

still

occupy

sees that all objects

it.

Neverthe-

definite posi-

events happen at definite times.

*

Scary Physics

The world is described by the equations of quantum mechanics, which don’t tell you for certain what is where. Objects can no longer be thought of as having definite positions or speeds. Maybe even cats can no longer be thought of as

definitely alive or dead.

Join the Flat Earth Society!

We

have

all

had

our ideas

to revise

many

times in order to attain a

proper grasp of physics. Each time, some things that were previously believed true

had

to

be accepted as

false,

mations to the new, better truth. Luckily, remarkably well with learning in

any subject, not

just physics,

signed to prepare your

human

beings seem to cope

this way. Serious students

become hardened

“Everything you were taught

say:

or at most as mere approxi-

last

mind for the

of almost

to hearing a lecturer

year was nonsense, a story de-

real truth,

which

is

”

as follows

However, not everyone can ascend the paradigm ladder successfully.

Back when

I

was a

college freshman, a fellow student jokingly

wrote to the agony column of one of along the lines

for

it.

newspapers

of:

“Dear Marje, I believe the earth

me

Britain’s tabloid

is flat,

and

my friends make fun of

Please help me.”

Back came the

reply:

“Do not worry. There are many people who feel exactly as you do. The

letter

went on

to give details of a Flat Earth Society,

met weekly or monthly

in

.” .

.

which then

—

London. This was some 20 years ago

al-

ready quite some years after beautiful, high-quality photographs of the

round Earth taken by various

sets

of Apollo astronauts had started

appearing in practically every newspaper and magazine on the planet. I

recently

went looking

for Flat Earth societies

still

in existence with a

view to interviewing some of their members. Alas, either the preva-

112

/ Schrodinger s Rabbits

lence of orbiting astronauts or other factors appear to have finally put

paid to this view as an organized school of thou^t. Although you will find many spoof references on the Web, the last sincere Flat Earth Society seems to have expired

some yeax-s

ago.

There are useful lessons to be learned from the flat-earth hypoththreatened by esis, however. Because almost nobody nowadays feels

we can look at the difficulties in going from one worldview to another more clearly and dispassionately than might be the case with some of the steps we will have to take later.

the concept that the world

The

is

a sphere,

durability of flat-earth belief shows

new

concept, even one that

is

how hard

stand from infancy that the universe taining three-dimensional objects. is

very large,

curvature of the Earth

is

I

view,

is flat”

happen

childhood. Australia

I

its

is

It is

senses. After

which

also basic to

curvature

it

can

still

is

understand that

if

very small, so that the

starts as

be disconcerting to abandon the

our default perspective.

know this because when I was

and back by ocean

voyage, the only one

we under-

a three-dimensional place, con-

be able to remember unusually

to

all,

not easily noticeable by inspecting your im-

mediate neighborhood. Yet

“world

can be to accept a

well within our capability to visualize

and does not contradict the evidence of our

a circle or sphere

it

liner,

and

I

we took during my

two,

far

back into

my own

my family traveled to

have clear memories of the childhood.

I

can remember

how profoundly disconcerted I was to be told that, even though people in Australia were standing upside down relative to people in England, they did not

fall

off the world because “gravity

is

a force like

magne-

tism that pulls you toward the middle of the Earth wherever you are.” I thought that when we arrived in Australia I would jeeX upside down,

but in a

much

like a character

using magnetic boots to walk on the ceiling

cartoon film, there would be a spooky force pulling

my

feet

up

toward the ground. Told that the Earth was turning and rushing through space at great speed, I went down to the bottom of our garden, far from the noise and vibration of the road

could not

feel

traffic.

Even

there,

I

the slightest sense of motion.

By now, you

are probably smiling at the naivete of

my two-year-

old self You no doubt have a clear mental image of the Earth as a sphere, illuminated by sunlight on only one side at any given moment.

A

Desirable Locality

and pulling everything on the force

and the

we

local

Some ment

call gravity.

at first

fact that the

is

113

surface toward

Of course,

time of day,

readers will

its

/

geometrical center by

the local direction of

different

remember

its

on each

own

their

part of the surface.

discomfort and amaze-

being told that the world was round.

notion of the

thousands of years

flat

Earth clung in

after scientists

knew

rian Jeffrey Russell has thoroughly

that

i^

It

many was

it

^ historical minds

people’s

spherical. Histo-

debunked the myth

cient Greeks’ discovery that the Earth

downward,

was round was

that the an-

either forgotten,

or opposed by any mainstream church, during the so-called Dark Ages.^

Throughout recorded European

mainstream natural

history,

philosophers have never seriously doubted that the Earth

The only informed debate

in

is

a sphere.

Columbus’s day concerned exactly what

the diameter was. But that did not stop huge ferring the notion of a flat Earth, almost

vising one’s ideas can be painful even

up

numbers of people

pre-

until the present day. Re-

when

the

new

picture

well

is

within our intuitive capacity to grasp.

Action at a Distance In historical terms, the junior school period represents a giant leap

forward: from the Middle Ages to the Newtonian worldview, which

dominated from the 17th

to the 19th centuries.

I

suspect that to

many

people, this intermediate period represents a kind of golden age or

comfort zone. The workings of the solar system, the nature of gravity, the basic rules of mechanics involving

momentum and

friction,

were

very well understood. But no one stopped to worry overmuch about the nature of space respect to

and time, which were assumed measurable with

some kind of absolute

fixed dimensions of space,

grid or framework.

and one of time, and

We lived in three

that

was

that.

And

although some questions about the nature of light, and a few oddities like

magnetism, remained obscure, these were mere

details that

could

be overlooked. I

would beg

to disagree.

The deceptively

ture actually robs us of something

beyond

friendly

price, the

Newtonian

pic-

key feature whose

assumption enabled us to make sense of the universe from the cradle.

JJ4

/ Schrodingers Rabbits V

and

that

formal

is

what

name

shall call the principle of locality.

I

That

for the rule, “Things affect other tilings only

is

a

more

when

they

are very close to then).” In our cradle physics, the force of gravity

not troubling from that point of

’^iew,

because

it

was

was assumed to be

and unidirectional, not coming from any particular object. But once the force of gravity is understood as due to the Earth’s mass

universal

in fact, the

sum

of tiny attractions from

all

the trillions of quintillions

of quintillions of particles that the Earth comprises, acting over a range

of many thousands of kilometers

—then we have the phenomenon

that

Hooke and Newton called “action at a distance.” Newton assumed corhad an

rectly that gravity at great distances,

incorrectly that

its

effectively infinite range,

becoming weaker

but never reducing to zero, but he also assumed so that moving an obeffect was instantaneous

ject a million miles

—

away would

instantly

change the

effect its gravity

had on Earth.

The Friendly

Field

Gravity was not the only nonlocal force in the Newtonian world-picture. Two other kinds of action at a distance were also known, although they appeared to affect only certain kinds of matter. These were the forces that we nowadays call electrostatic and magnetic. Although both

phenomena had been trostatics

by Charles

studied before, magnetism by Gilbert and elec-

Du

Fay, British scientist

search in the early 19th century went

School pupils today

still

it is

less well

at a distance,

between

instinctively

and wondered

electricity

opposed

if electric

explained in any other way. This led fields

deeper.

and magnetism,

known that his deeper motivation was

He was profoundly and

re-

learn of Faraday the experimenter, inves-

tigating the intimate relationship

but

much

Michael Faradays

to the notion of action

and magnetic

him

philosophical.

forces could be

to the concept of lines

and

of force. As a simple example, consider the two pith balls shown

in Figure 8-1.

Both

balls in Figure

another as shown. acts

on the other

8-f are positively charged and they repel one

One way

to think of

what

is

going on

directly at a distance, as indicated

is

that each

by the double-

A

Desirable Locality

/

115

FIGURE 8- 1 Do charged objects repel one another by direct force, as on via fields, as

on the

arrow on the lets

an

you consider

or

But an alternative interpretation, shown on the

right,

an

invis-

that each charged ball surrounds itself with

extends through space, which

Each

electric field.

ball

the field that surrounds as operating

left,

right?

left.

ible field that

the

it.

is

call

pushed, not directly by the other, but by

Similarly,

on one another

we would nowadays

you can think of magnets

directly, or as

either

being surrounded by mag-

netic fields.

Faraday’s contemporaries were initially scornful of his field notion.

It

seemed

to violate

sary, invisible entity?

Occam’s razor; why postulate an unneces-

Some modern

philosophers of physics might

have dismissed the idea for a rather different reason, that the question of whether the electric interpretation. If erts

on

an

field

was

electric field

real or is

not was merely a matter of

by the force

discernible only

it

ex-

a charged body, then surely the question of whether the field

“really” there

when no charged body

is

present

gels-on-the-head-of-a-pin kind of proposition.

is

is

an untestable, an-

We

are therefore free

to think of electric forces in terms of action at a distance or in terms of fields, as

we

please.

The only thing that deserves

to

be called

real

is

the

mathematical algorithm that enables us to calculate the forces exerted, the inverse-square rule.

116

/ Schrodingers Rabbits \

Fortunately for scientific progress, Faraday was not sophisticated

enough

to dismiss his field notion for either of these reasons. Fie felt

very strongly that electric and magnetic fields were real things.

And as

mere interpretation turned

so often happens in"science>what started as

out to have real and testable consequences. Faraday speculated that if not change a field had a reality of its own, then moving the source need the state of the whole field instantaneously. Just as real Substances have finite elasticity,

and transmit impulses

when you tap one end of a wooden an instant

until

later

—so might

at finite

ruler, the

electric

speed

—

for example,

other end does not

and magnetic

fields.

move

Faraday’s

further, to speculate that radiation

extraordinary intuition led

him

such as light might in

be vibrations in the lines of force of his

that gravity also

field,

fact

might be transmitted

at finite

speed through the

medium of a field, and even that the particles of which matter is made might be no more than knots

in these fields.^ Arguably,

he thus pre-

dicted important elements of both special and general relativity,

and

even string theory. Fiowever, Faraday lacked the mathematics to develop his predictions quantitatively. This

was done by the Scottish

scientist

James Clerk

Maxwell. Like Einstein, Maxwell was primarily a visual thinker.

Fiis

and

vol-

insights were developed in terms of lines

and

areas, surfaces

umes, topology and geometry. Although he was very competent in math, it was his servant, not his master. The entities that he described

had

to have visualizable meanings, even

ible things

—

a lesson for today’s

though they described

quantum

physicists.

invis-

Thus he was soon

deriving such useful quantities as magnetic pressure, measured like ordinary pressure in pounds per square inch, and magnetic energy. It

turned out that a strong magnetic

field

energy, just like a compressed gas, so

There

is

a

symmetry between

could be thought of as storing

much

electric

per unit of volume.

and magnetic

fields that

is

normally obscured because in the laboratory we can find plenty of protons and electrons but no particles carrying an electric charge

—

—

corresponding ones with magnetic charge. Nevertheless, an field

in a

can also be created by a^change in a magnetic

field,

electric

and vice versa,

yin-and-yang relationship. This led Maxwell to an intriguing pos-

sibility:

Could you

create an electric-magnetic field that existed inde-

A Desirable Locality / 117 pendently in

its

own

with no associated physical object? The

right,

answer turned out to be that such a phenomenon could

would never be

stationary:

like a

wave or ripple

lated

from two known

permittivity exactly

at a

It

would propagate through empty space

speed that was very high, but could be calcuof the vacuurn, called the

electrical properties

matched the measured speed of light.

“Treatise

on

tragically

Electricity

young,

at the

age of 48, but his famous

and Magnetism” was developed by colleagues and others into

Fitzgerald, Oliver Heaviside, Oliver Lodge,

George

complete and beautiful picture. Electric and magnetic thought of

as represented

—we now

volume of

call

space. If

by

them

little

vectors

—

it.

can be

associated with every point in a

you draw an imaginary surface around that

vol-

flux arrows going

and out of the surface defines the net amount of

within

fields

a

arrows having magnitude and di-

ume, then the difference between the quantity of into

but

and the permeability. The speed of the predicted wave

Maxwell died

rection

exist,

electric

charge

More complicated geometrical calculations yield more subtle

quantities, such as the energy associated with a given

netic field.

And

many other

so

we can

devices

But what

is

volume of a mag-

design the electric generators, motors, and

on which our modern

important to us

is

civilization depends.

that, at least as far as electric

and

magnetic forces were concerned, Faraday and Maxwell had abolished action at a distance and restored locality.

yond reasonable doubt the were

real

enough

They had demonstrated be-

existence of fields

to contain energy of their

—

invisible entities that

own

—and

that objects

interacted not with far-off things, but only with the electric netic fields immediately surrounding them.

There

is

and mag-

no instantaneous

electromagnetic interaction at a distance: With sufficiently delicate instruments, you might be able to detect the field due to a magnet a million kilometers away from you, but that magnet, the magnetic field

if

around you

Any such change can propagate out only and the

maximum speed

is,

somebody suddenly moves will

not instantly change.

like a ripple at finite speed,

by definition, the speed of light, the speed

of an unencumbered electromagnetic wave in free space.

There are

at least three

reasons to celebrate Faraday’s and Maxwell’s

abolition of the action at a distance of the

Newtonian

picture.

The

first

118

is

/ Schrodingers Rabbits

simply that such remote action

is

upsetting to our early intuition,

our instinctive baby expectation that objects ^an interact only by I touching. I can still remember how spooky it was when, as an infant, a horseshoe fnagnet could snatch

shown how

was

first

bar

when

it

was

still

a

good inch away

frorn

it.

up

its

The touching

keeper

rule

is

of

to course only a rule of thumb that evolution has found advantageous what might install in us, but it is a very useful rule for simplifying

otherwise be an incomprehensible world.

The second reason rectly affect

we can actions

is

the theoretical worry that

one another from

far away,

it

if

objects can di-

undermines the hope that

ever properly test the laws of physics by experiment. If the of processes on, say. Alpha Centauri can directly and instantly

behavior of equipment in a terrestrial laboratory, raising the can never possibility of self-amplifying feedback interactions, then we

affect the

perform an experiment on

a truly isolated system.'^

simply that instant long-range interactions make it much harder to construct simple predictive models of the ones world. This applies to all kinds of models, including traditional

The

third reason

is

based on fearsome-looking differential equations, but is easiest to see by using a more modern device, the cellular automaton. Ever since the

computer was invented, the cellular automaton has been the physicist s volume tool of choice for modeling systems that occupy an extended of space—which is to say, just about everything the real world contains,

be

example

it

is

a solid, liquid, gas, or

shown

in Figure 8-2,

something more

which depicts

exotic.

A

simple

fluid flow.

can calculate forward from the picture on the left to that on influthe right quite economically, provided that each cell is directly enced only by the cells immediately around it. For example, to find the

We

new state of the

cell

which

is

shown shaded on

the right,

into account the previous state only of the cell itself and

we need take

its

immediate

shown lightly shaded on the left. If nonlocal influences work, we would have to take into account the state of all the

neighbors, as

were other

at

cells, in

rection,

principle extending an indefinite distance in every di-

and the amount of calculation involved would be

the other

hand there

are ncv nonlocal influences,

it

vast. If

on

opens the door not

only to the idea that the universe can be economically modeled, but

A

z -4 -4 z -4 zz -4 z -4 -4 \ z -4 z z Z z - zz z -4 z z Z' z \ z z -4 z -4 -4 -4 z -4 \ z -4 -4 z \ - z z -4 -4 z s. z

--

/•

\ \

/*

-

/"

\\ FIGURE

/ 119

-

\ \

-

Desirable Locality

-

/

-4

-4

8-2 Modeling the flow of a turbulent fluid by computer simulation: one

time step takes you from the

left

picture to the right one.

even to the possibility that

it

might actually be something

as under-

standable as a kind of local cellular automaton, a hypothesis return to in the

we

last chapter.

Faraday himself will remain an inspiration to us in two ways.

immense importance. But even more,

things, has turned out to be of

shall

be

sense,

—

First,

on nearby

the specific concept of locality, that forces can operate only

his attitude

will

stubborn practical man’s insistence that the universe

a

intelligible,

however

and

shall

conform

difficult this goal

to

our notions of

might sometimes seem

—

commonwill

guide

us in our quest.

But

now it

is

time to graduate from high school

A Moving Perspective Maxwell’s brilliant work had of course tion hanging: Given that light

medium

is

left

one interpretational ques-

an electromagnetic wave, in what

can the wave be considered to be traveling? After

all,

sound

waves are a movement of air molecules, and sea waves a movement of water particles; even though light waves are rather more abstract,

some kind of supporting medium? As

surely they

must

back

mid- 18th century, the great mathematician Euler had hy-

as the

travel in

far

120

/ Schrpdingers Rabbits N

pothesized a “sunlight

is

medium

to ether

what sound

space, called the ether,

all

to

is

and

that

air.”

^ th^ interactions between ether

However weak ter,

that filled

and ordinary mat-

property— its speed with so, imagine that the ordinary atmo-

ether should have at le^st one detectable

respect to Earth. To see

why this is

ability to carry

sound,

wind blowing. Sound

travels

sphere has no detectable properties except for

and you want in air at

to

know whether there

330 meters per second, so

3.3 kilometers in radius circle,

the air

and

if

set off

is

a

you

its

station observers in a circle

an explosion in the middle of the

later if each observer should hear the bang exactly 10 seconds However, if there is a gale blowing from the north at 30 is still.

observer in meters per second, the sound reaching the northernmost seconds to reach him, the circle is delayed by about 1 second, taking 1 1

whereas

it

will reach the

southernmost observer

1

second

early, after

wind of any speed and direction causes some others. observers on the circle to hear the sound earlier than respect to Earths In exactly the same way, any ether wind with

only 9 seconds. In

fact, a

surface should be detectable because light

would

travel slightly faster

some directions than others. No one knew whether the solar system because the was moving or stationary with respect to the ether, but continually Earth orbits the Sun at some 30 kilometers per second, in

changing direction as

it

does

so,

it

could not possibly be stationary

the apparent with respect to the ether the whole time. A variation in been easily speed of light on the order of 1 part in 10,000 should have detectable with late Victorian instruments. It

was Maxwell who

first

described a practical experiment to de-

wind, but he died of cancer before it could be carried he extraordinary to think that had he lived a little longer,

tect this ether

out.

It is

might well have anticipated Einstein

in the

development of

special

relativity.

wind could be detected when the experiment astrowas eventually performed by Michelson and Morley. Precise

Of course, no

ether

the idea nomical observations ruled out other possibilities, such as of ether along with it. that Earth somehow dragged the local envelope In that case, the effects of ether current should

show up

tions in the timing of such events as eclipses.

It

as subtle varia-

could hardly be the

A

case that

all

Desirable Locality

/

121

the ether in the solar system was being dragged along in

measurements on

step with our particular planet. Similarly,

stars that

orbited one another rapidly ruled out the idea that light traveled with a fixed speed relative to really did It

source, like a bullet fired

its

from

a gun.

There

appear to be a deep paradox here.

was of course Einstein who solved

that space

and time

observer in such a

it,

with the bold postulate

are not absolute, but vary with the

way

speed. For example,

if

that light always appears to

move

at

constant

a spacecraft were to pass Earth at very high

speed, then from our point of view

clocks

its

would appear

ning slightly slow, and the ship and everything aboard contracted in

motion of the

it

to be run-

would appear

direction of motion. Conversely, observers

its

on the

spacecraft

would perceive the

relative to

our viewpoint. In general, we would not agree with the oc-

rest

of the universe as spatially distorted

cupants of the craft on either the distances and directions of objects or the timings of events that

These objects

perspective. jects

sound very

effects

moving

we could both

at

observe.

bizarre, but the apparent distortion of

very high speeds

really just

is

an unfamiliar kind of

Even the most basic rule of perspective

look smaller

—

—

that faraway ob-

not hard-wired into our brains. Here

is

account, from an anthropology textbook, of a

brought outside his native

forest for the first

Turnbull studied the Bambuti pygmies

who

a true

Bushman who was

time in his

live in

is

life.

the dense rain forests

of the Congo, a closed-in world without vast open spaces. Turnbull

brought a pygmy out to a vast plain where a herd of buffalo was grazing in the distance.

before;

when

The pygmy

said he

had never seen one of these

told they were buffalo, he

insects

was offended and Turnbull was

accused of insulting his intelligence. Turnbull drove the jeep toward the buffalo; the pygmy’s eyes

widened

‘grow’ into buffalo before him.

used to deceive him.

Does argue that

amazement

He concluded

as

that witchcraft

make

reality

was being

harder to visualize?

I

would

does not in any fundamental way, because we already had

to get used to the fact that objects look different spectives,

he saw the insects

^

special relativity it

in

and

that different observers

different per-

might naturally have used

ferent coordinate systems, long before relativity relativity asks us to take

from

came

only one small further step

—

dif-

along. Special

to the idea that

122

/ Schrbdingers Rabbits %

the observer’s natural coordinate system

and perspective viewpoint

vary not just with position but also with speed,

he universe can look

twQ people in the same place, if they are moving at differ^just as we alr&^dy know that it might look different velocities

different even to

—

different ent to observers in different places. But things only look If an cause and effect, the flow of events, are the same to all observers. in occupant of our imaginary spacecraft makes himself a cup of tea,

our telescope we see him putting the

kettle on, getting a teabag,

and so

he seems to move rather slowly, and the kettle looks rather have squashed, this is just an extension to the rules of perspective we

forth. If

From

always accepted.

usual shape and he

The aspect of cept

is

the astronaut

s

doing everything

is

point of view, the kettle at

normal speed.

special relativity that initially

the idea that time can appear to flow

moving

fast

is its

seems hardest to ac-

more slowly

with respect to yourself. You might find

it

in a

frame

helpful here to

even in a consider that Doppler effects would produce similar oddities

Suppose that a train is one-tenth the speed of sound, 70 miles an

nonrelativistic universe. First, consider sound.

traveling toward

hour.

than

You

at

will hear the pitch of its whistle as

really

it

you

is.

If

about one-tenth higher

your ears were good enough to hear

a conversation

would taking place aboard the train, the pitch of everybody’s voice seconds’ worth of also sound higher, and moreover, you would hear 10

word conversation in only 9 seconds, because the sound of the last would have less distance to travel to reach you than the sound of the word, and so would reach you in less time. If you were blindhappening folded, it would seem exactly as if life aboard the train were

first

passed 10 percent faster than normal. After the train ceding, everything

the

same

re-

you heard would seem correspondingly slowed by

factor.

In exactly the

same way, even

was an ether wave,

life

in a universe in

than normal

—or

which

light really

aboard a spaceship coming toward you

tenth the speed of light would look as faster

you and was

if it

10 percent slower

at a

were happening 10 percent if

the spacecraft was reced-

our universe, you have to add on the relativistic correction as an additional factor to thi» Doppler effect, an additional slight slowing light. of events on board the craft. Actually, even at a tenth the speed of

ing. In

A the Doppler effect

is

Desirable Locality

much

/

123

bigger than the relativistic correction:

only at more than half the speed of light that the overtakes the Doppler one. There

really

is

It is

relativistic correction

nothing surprising about

events in a fast-moving frame of reference seeming to happen at a ''4

different rate.

General

relativity asks us to stretch

accept that the fabric of space just as the Earth’s surface

An

is

is

not

warped by the

flat

under our

object falling freely under gravity

line in the

The

warped space

subtlety that

I

adequately explained in

our minds a

is

force

feet

some of the

we

and

call gravity,

but bends

slightly.

actually traveling in a straight

that immediately surrounds

think confuses

further

little

many

texts

I

people,

have seen,

ing an object encounters once again depends

it.

on

its

and

is

that

that the

is

not

warp-

speed as well as

its

position. For example, consider three spacecraft at a point 100 miles

above the Earth traveling gravity.

Each

at different

speeds but

from

travels in a straight line

with different

results, as

shown

its

all falling

own

in Figures 8-3a-d.

freely

under

point of view, but

The sounding rocket

back to intercept the Earth’s surface (shown as a thick black

falls

line),

the orbiting satellite maintains a constant distance from the surface, the interplanetary spacecraft traveling at escape speed increases

its

dis-

tance from the surface. Note that because photons themselves travel so fast

compared

to Earth’s escape speed,

vicinity of Earth actually sees

what any observer

through a telescope corresponds almost

exactly to the “flat-space” view, irrespective of the observer’s locity. If

tron

we

in the

own

ve-

lived in the vicinity of a dense massive object like a neu-

star, general-relativity-related

perspective effects

would be

familiar to us.

Once we have accepted

the

new

perspective rules, the relativistic

universe actually gives us a priceless benefit.

emphasis that has been lacking

It

restores locality with

in every picture since

an

our original nurs-

ery physics. Objects interact only with things that they are physically

touching

—granted

that those things are fields rather than physical

objects. All forces, electromagnetic

through the

medium

of

fields,

and

and disturbances

rather special distortion-of-space field that

no

faster

than

light.

There

is

other, exert their effects

no action

is

in fields

gravity

at a distance.

—even the

—can propagate And

that

makes

V

124

/ Schrodinger’s Rabbits

X

N

d

FIGURE

8-3

View of

a

sounding rocket, a

satellite,

and an interplanetary space-

100 miles above Earth’s surface. In fact, each object line with respect to its own perception of space. craft

(a) Flat-space

view

(b)

Space as experienced by the pounding rocket

(c)

Space as experienced by the

(d) Space as experienced

satellite

by the interplanetary spacecraft

is

traveling in a straight

A

Desirable Locality

/

125

the universe relatively straightforward to understand a cosy place in

which only things

in

and model.

It is

your immediate neighborhood

affect you. If only

we could

integrate

quantum

could perhaps play against the gods on

our brains are wired to understand.

into this neat local picture, fair

we

terms, in an”^afena which

V

Chapter 9

INTRODUCING MANY-WORLDS

X

W

henever we tally,

we

ing as a

test a

find that

small piece of our universe experimen-

up

until that

chunk of Hilbert

moment it has been behav-

space, developing not as a single

but as a nest of interacting probability waves. This description of nature is by far the most accurate that has ever been achieved. Quan-

history,

immensely precise predictions of timings of microscopic processes, which have been confirmed

tum theory makes and

freqitencies

to an astonishing

possible

number of decimal

places.

The waves of Hilbert

space are simply the waves Schrodinger derived a lifetime ago, although we now have better mathematical tools (and of course, computers) to help us

work out

many-worlds interpretation that

what the math

tells

us

their behavior.

The essence of the

is

breathtakingly simple. Let us assume

is

correct.

We

can then explain what

is

going on in terms of three emergent phenomena: entanglemenU decoherence and consistent

The math implies bouncing around

histories.

that an isolated system, say, a

bunch of atoms

in a sealed container, explores all the

ways the atoms

not a question of atoms surfing guide waves, as in the original picture we tried to construct, but of the atoms themselves trying out all the possible' paths, going every-which direction. The

might

go.

It is

126 %

Introducing Many-Worlds

/ 127

waves of Hilbert space explore every possible way the system might develop. If

we put

second isolated system containing some kind of

a

observation apparatus in contact with the

system, neither under-

first

goes any kind of collapse. Rather, the mathematics of entanglement tell

us that the high-probability areas of the joint Hilb^rKspace thus

created will develop as consistent histories. For example,

system

and the

is

atom (one

a radioactive

large system

is

ticle is detected,

the small

that can spontaneously split apart),

a radiation detector with

consisting of a capacitor that

if

memory

an electronic

becomes charged when

a radioactive par-

then the states atom-split-capacitor-charged and

atom-whole-capacitor-uncharged quickly become

much more

likely

than atom-split-capacitor-uncharged and atom-whole-capacitorcharged. Likewise,

if

the small system

and the large system

is

Schrodinger’s cat apparatus

a cat-loving astronaut, live-cat-happy-

astronaut and dead-cat-sad-astronaut live-cat-sad-astronaut

is

become much more

likely

than

and dead-cat-happy-astronaut.

Why are the happy and sad versions of the astronaut not aware of one another? The mathematics of decoherence tell us that the

interfer-

ence between developing outcomes that are significantly different

above the microscopic difference slit

is

that

level fade

very rapidly. History lines whose only

one electron has gone through the

left slit

of a two-

experiment instead of the right one interfere with one another

where

quite significantly, but history lines different positions (such as the

lots

atoms of the

of particles are

cat’s

all

body and the

in

elec-

trons within the astronaut’s brain in the above example) interfere with

one another only

to a very tiny extent.

As the philosopher Daniel

Dennett and others have pointed out, the things that we consider to be real,

including ourselves, are simply stable, persistent patterns:

happy-astronaut-live-cat pattern that particular pattern of her

—

is

is

one such. As

far as she

—

The

that

is,

concerned, she inhabits a single his-

tory in which the cat was lucky and lived.

The many-worlds

interpretation

is

sometimes claimed to beat

others by Occam’s razor, on the grounds that cal

assumptions. Accepting

sary to accept that the like

same

bunches of atoms,

it

it

requires

all

no new physi-

requires only the moral courage neces-

rules that apply to small isolated systems,

also apply to larger isolated systems

without

128

/ Schrodinger’s Rabbits

limit, therefore including the largest possible

as a

one

—our universe taken

whole.

The no-assumptions claim can be

challenged. In fact, even the

most prominent supporters of mjj.ny-worlds nowadays acknowledge that

some

postulates

more

issue we’ll look at in

ing for

it

to

accommodate

the theory, an

more go-

detail later. But' many- worlds has

than Occam’s razor. Chapter 7 prepared us Tor the

there might be

more

must be made

many ways

to look at physical reality,

correct than the others. But

many-worlds

fact that

none uniquely

is still

preferable to

other interpretations for the same reason that the cabin boy’s ticktack-toe was a better It is

easier for

game than

the ideas of the other crew

our minds to grasp.

It

members.

enables us to keep to the intuitive

and other great physicists have struggled universe of three dimensions of space and one of time,

picture that Faraday, Einstein, to preserve, a in

which nothing

is

random and

That’s quite a claim. Let us

we

will

come

to

some

locality reigns

first lay

reservations

resolve our Principal Puzzles of

supreme.

out the evidence in

later.

We

are

Quantum. We

now

its

favor;

in a position to

will take

them

in re-

verse order.

PPQ4 Why

does reality appear to you to be the world in a single specific

pattern,

when the guide waves should be weaving an ever more tangled

multiplicity of patterns?

Answer Your mind

in a specific state

physically,

your brain in a

atoms and

is

a pattern of information

specific state

is

—or speaking

a pattern of positions of

The mathematics of decoherence predict that say, bethat initially differ by a trivial amount

electrons.

two brain patterns

—

cause one particular photon happened to be transmitted rather than very reflected when hitting youB cornea, thus reaching your retina

—

quickly cease to have any significant effect ference grows.

on one another

as the dif-

Introducing Many-Worlds

/ 129

(Oxford philosopher Michael Lockwood prefers many-minds. His

which

point: the large Hilbert Space within

all

physically possible

histories unfold contains mind-patterns that have seen

different versions of events.

However

sophical complications; so,

shall stick

A mind is just an

I

this

and recorded

viewpoint leads to philo-

with a physicist^ f>erspective:

information package embedded in a world-line.)

PPQ3 Why does the universe seem to waste such a colossal amount of effort investigating might-have-beens, things that could have

happened but

didn’t?

Answer It

does not waste any effort investigating might-have-beens. The inter-

ference patterns that

things that didn’t

seem

happen

to demonstrate that the universe tried out

—how did the universe know whether the

bar-code reader would have registered the chicken going through the other

slit?

ever, the

—correspond

to

outcomes that

in fact also

happened.

How-

world patterns in which they happened decohered rapidly

from those

in

which they didn’t as soon

surement occurred. We

as the interaction

we call mea-

now understand that taking information about

a system, recording the result

permanently in a larger outside environ-

ment, is actually what causes decoherence. The terms “permanent” and “larger outside environment”

by them

might sound

like a cheat,

an environment containing enough

is

bottle they

all

just

all I

mean

particles that a sponta-

neous reversal of the recording process becomes of ink on a sheet of paper

but

happening

unlikely, like the dots

to leap

back into the

came from.

PPQ2 Spooky quantum or that

quantum

links

seem

to

imply either faster-than-light signals

events are truly random.

V ‘

«

130

/ Schrodingers Rabbits K

Answer Assuming many-worlds, the laws of physics do^not imply any randomness at all. When^for example, a photon hits a polarizer, the result is

quite deterministic.

space,

one

in

gives -ris^' to

which the photon

There

reflected.

It

will also arise

is

two

two event-patterns

in Hilbert

transmitted and one in which

it is

different patterns corresponding to

the present “you,” matching each outcome.

PPQ Spooky quantum

links

seem

to

1

imply either faster-than-light signals

or that local events do not promptly proceed in an unambiguous at

each end of the

way

link.

Answer Locality has always been claimed as a benefit of the

many-worlds ap-

proach, but the point was not proven until quite recently, in a brilliant

paper published in 2000 by David Deutsch and Patrick Hayden.^ Here,

we

however, tions of

will give a

EPR can

arise

nonmathematical picture of

from

how

the correla-

local effects alone.

To explain the process, we

will

go back to the lottery cards of

Chapter 1 and expand on the notion that causing quantum decoherence here, by scratching a lottery card and observing

—

whether you get a black or

a white spot

—

gives rise not simply to

two

worlds, but two sets of local worlds. Later,

we will

consider whether these sets should really be consid-

ered infinite, but for illustration purposes

the spot

shall

assume

that each

scratched,

it

gives rise to exactly 100 versions of local

which the spot

is

white and another 100 versions in which

time a spot reality in

we

is

is

black.

So when you go into your booth to play the lottery

game, when you scratch your card you might think of yourself as ating 200 versions of your booth, each floating little bit like

Dr. Who's Tardis in the old

BBC

around

cre-

in a grey void a

television series. Half of

these booths contain versions of you holding a card with a white spot.

Introducing Many -Worlds

/ 131

and the other half have versions of you' holding a card with

a black

spot.

Your partner has similarly created 200 versions of her booth. The subtle bit

is

how

tent histories.

the various booths get allocated to different consis-

Here

is

a crude

metaphor

for

what occurs.Tifiagine

that

each version of each booth stretches out a ghostly tendril. At the the

end of each

number

tendril

is

a label with information like, “left booth, spot

3 scratched, revealed color white.” Shortly

we are going to

use

the tendrils to pull together 200 complete classical-looking worlds,

each containing one booth with you in partner in

it.

We

it

and one booth with your

can make the correlations between your and your

partner’s colors anything

we

like

simply by joining up the tendrils in

an appropriate way. For example,

if

you have both picked the same

spot,

we

pair the

100 versions of you holding a black card with the 100 versions of your partner holding a black card, and the 100 versions of you holding a white card with the 100 versions of

card.

The

posed If

results all

match

in

all

your partner holding a white

the resultant worlds, as they are sup-

to.

you each pick

a spot at 90 degrees to your partner’s,

we

pair the

100 versions of you holding a black card with the 100 versions of your partner holding a white card, and the 100 versions of you holding a

white card with the 100 versions of your partner holding a black card.

The

results are opposite colors in all the worlds. If

have

you and your partner pick spots one place apart

if

you are trying

you holding

to

win the game

a white card with

—we

pair just

—

as

you

will

one version of

one version of your partner holding a

black card, and just one version of you holding a black card with one version of your partner holding a white card.

Then we

pair

up the

remaining 99 versions of you holding a white card with the 99 versions of your partner holding a white card,

and the 99 versions of you

holding a black card with the 99 versions of your partner holding a black card. Everyone

is

accounted

for,

and you have won

in just 2

worlds out of the 200, as expected.

Of course

this sorting

of diverging worlds does not really involve

— s>.

132

tendrils with labels

/ Schrodingers Rabbits

on them.

the world containing

a process

It is

you comes

whereby each version of

to be potentially

more and more

af-

by one particular version of the world containing your partner, and less and less by the other versipjis. You could imagine the process as analogous to pulling entangled skeins of wool gently apart into fected

sheets; or even as resembling the biological process of meiosis, in

which chromosomes are duplicated and then

in

due course spliced

back together in appropriately matching ways. But the key point is that nothing happens that would require the propagation of fasterthan-light influences.

The process of quantum

collapse

—the process

of scratching the card, and even your consciously seeing the result

At that point your Tardis-booth already “knows” what kind of partner is appropriate for it to hook up to. But it does not need to exchange information with the maybe far-off partner booth at that can happen

point. This

fast.

the difference between selecting a partner in a video

is

dating booth, and immediately writing

telephone number, which faster.- than-light is

not.

down

(or even dialing) their

perfectly possible,

is

and having an

actual

exchange of messages with your partner- to-be, which

Many-worlds respects the

spirit as well as the letter

of special

relativity.

With all this going for

it,

you might expect

that the case for

worlds would be considered cut and dried. From Oxford, where so

many

And

wide

yet

many-worlds

scientific

American

is

community.

physicists

perspective in

of the leading supporters of many-worlds

(some of whom we’ll soon meet) way.

my

many-

who

live

and work, it sometimes

feels that

not universally accepted in the world-

Max

Tegmark, one of the few leading

actively supports

many-worlds, has pub-

lished the following results of an informal poll he took at a recent

international conference

—

Copenhagen: 4

on quantum

Believers in the

physics.^

modern Copenhagen

tation in the broadest sensef the idea that the

wave equation

interpre-

unmodified Schrodinger

gives rise to a collapsed single reality when perceived

a conscious observer.

%

by

Introducing Many-Worlds

/

Collapse mechanism yet to be discovered: 4 that the Schrodinger

physical collapse

meet

in

(for example,

Chapter 14) that gives

—

Believers in the idea to include

Roger Penrose’s, which

we’ll

some form of Bohmi*S^ilot- waves

traced out by particles surfing

is

some

rise to a single- valued reality.

Believers in

notion, that a single reality

waves that

—

wave equation must be modified

mechanism

Pilot waves: 2

133

in a sense explore all the

on guide

developments that do not

really

happen.

Many-worlds: 30

—

Believers in the idea that collapse never hap-

many

pens, and the universe keeps exploring

which should be considered equally That looks pretty convincing so worlds, with the opposition

split.

different outcomes,

real.

75 percent vote for many-

far: a

But there

a further figure: 50 (of

is

the total of 90) physicists in the hall were undecided, or at least unable to agree with

any of those four broad choices. That

In one sense, many-worlds

opposition to way,

it

it is

has a long

is

is

rather appalling.

becoming the only game

in

fragmented and dwindling. But looked

way

Only

to go.

—some

at

another

a third of the specialists in the field

were willing to stand up and be counted Let us look at the reasons

town. The

as

many-worlds supporters.

justifiable, others less so

—

for this

many-worlds

is

one of

situation.

One problem might

be, ironically, that

time. Back in

those scientific theories that was proposed ahead of

its

the 1950s, before most of the current generation of

quantum

cists

were even born,

Hugh

Everett

III,

physi-

student of the famous John

Wheeler, wrote a Ph.D. thesis outlining his proposal, which in retrospect seems astonishingly obvious: lapse occurs at

all?

Why

Why

assume

that

quantum

col-

not simply believe what the equations are

telling us, that the universe

is

tracing out

all

possible histories, rather

than just one privileged one? Everett cases, the

was able

to

demonstrate

that, in

simple but suggestive

development of the probability waves of Hilbert space tends

naturally to give rise to different branches of

outcomes whose subse-

quent histories the evolving wave continues to trace out. Unfortunately, at the time Everett was writing, the mathematics of

i34

/ Schrodingers Rabbits \

decoherence had (inevitably) yet to be properly worked out, and

was not

entirely clear

tinue to diverge

and

why

histories that

interact with

it

were different should con-

one another less and

less, as is

of

course the case. Thfs valid problenx-caused another physicist, Bryce de Witt, to try to advance Everett’s theories in a

was unhelpful.

and sought

a

It

was de Witt who

mechanism

that

way

coineci the

would cause

that in retrospect

term “many- worlds,”

different worlds to diverge

completely from one another, cleaved apart by outcome lines that had zero probability. slit

is it

We

can explain his idea with the version of the two-

experiment diagrammed in Figure 9-1.

The height of the wave function indicates that the particle involved more likely to turn up in some places than others, but at some points can drop to zero; interference cancellation is perfect, and the par-

ticle

should never be detected in such a position.

De Witt

interpret such points as fault lines, splitting the universe

into distinct versions, each corresponding to

pletely.

is

no point

They continue to

at

permanently

one of the possible

gions in which the particle might end up. This necessary. There

tried to

is

re-

neither correct nor

which outcome worlds diverge com-

interfere with

one another, although

in a

way

that decreases rapidly with time. But they never actually split.

FIGURE

9-1

De Witt viewed

zero-probability outcomes as giving rise to segre-

gated worlds, like lane barriers forcing automobiles to diverge toward different destinations at a road junction.

— Introducing Many -Worlds

When

Everett

first

developed his theory, he made no reference to

splitting worlds. Rather, his

many

cesses

theory describes a single universe that pro-

different versions of events.

grander vision of the universe guish

it

from the

single observer

1980s. This fibres

/ 135

—often

A good metaphor

for this

called the multiverse^ to distin-

single version of reality visible to a singteiis of these isj:he

huge amounts of radio telescope

SETI@home

data, to see if

project to process

any signal from any

part of the sky shows a pattern that might' indicate that

it is

an

intelli-

The SETI project has -already received plenty of publicity, but there are now a number of other distributedscreensaver projects to choose from. If you want to do something use-

gent signal from an alien race.

ful

with your computer’s spare

Screensaver Lifesaver

Web

site.^

moments you might

like to try the

This project involves screening mil-

lions of possible chemicals for useful biomedical effects, in particular

against cancer, by calculating to

them

to

dock with certain

while cause and

is

likely to

what extent

target molecules.

their shapes will cause

It’s

an extremely worth-

be the forerunner of an even more ambi-

Human Genome Project gives way to what has been called the Human Proteome Project, the huge task of identifying tious project as the

every biologically active molecule in the esting option

is

human

body. Another inter-

the Climate Prediction screensaver.^ This builds

the technique of ensemble weather forecasting. Nowadays,

on

when

a

weather forecasting center makes a prediction, it is never the result of a single computer run. Forecasters are aware of the possibility of the butterfly ^effect:

Would

a tiny change in input parameters have pro-

duced a completely different

forecast?

They therefore run

their

model

many times, each time with slightly different starting values because they know that their input data can never be perfectly accurate. If they get the same outcome every time, they know that they can forecast that weather with high confidence. If two or

ent results sure.

more

significantly differ-

come from different runs, they know that they cannot be so

When

a forecaster says that there

is

33 percent chance of rain

tomorrow, he may well be indicating that of 100 such simulations, about one-third ended in wet weather, the

The Climate Prediction screensaver ther. When predicting what the climate there are an

back

effects.

rest in dry.

takes the technique a bit furwill

be

like in

20 or 50 years,

enormous number of unknown variables governing feed-

How much

sunlight will be reflected back into space by

Harnessing Many-Worlds 2 / 159

clouds in a given scenario? By what percentage would a l^C temperature rise increase the melt rate of the Greenland ice shelf? will the

How much

in the salinity of the

Gulf Stream weaken per point of decrease

Northern Atlantic? And a thousand similar questions. The Climate Prediction project likelihoods.

building not a single forecast, but an"ertsemble of

They already have one

fly effect affects

day.

is

interesting result:

the climate, not just the weather

A kind of butter-

on some

particular

A very tiny change in parameters can give a whole region a mark-

edly different temperature and rainfall over a long period.

mate Prediction screensaver

is

beautiful

and somewhat

The

Cli-

terrifying to

watch, as a graphic of Earth shows the icecaps, deserts and forests shrink and grow in your particular

slice

of the future.

These kinds of distributed Internet projects might be able to cruit

up

upper

to several million

limit.

Even

if you

computers each. But obviously there

an

could persuade everyone on the planet to help

you, there are only a billion or so computers available. That

compared

is

re-

to the potential richness offered

is

nothing

by quantum.

Massive Parallelism To understand the benefits of quantum computing, we

will briefly re-

how a standard computer works. The heart of a computer is a device much like an old fashioned mechanical calculator, the kind that

view

had

a handle

on the

side that

you could turn

to add, subtract, or

mul-

numbers using wheels very similar to those in the odometer on your car dashboard. But a computer operates electrically, and it uses numbers based not on the decimal system, which has 10 different digits with successive columns representing units, tens, hundreds, and so tiply

on, but on the binary system, which has just two digits, zero and one,

and etc.

in

which successive columns represent

units, twos, fours, eights,

Figure 11-1 illustrates a simple binary calculation. Deutsch’s

initial

idea

amounts

perfectly ordinary binary calculator

to this.

Suppose we could take a

and place

it

in Hilbert space, en-

closed behind an impenetrable barrier like Schrodinger’s cat.

then arrange the digits poised in cat’s

Hilber t space

unknown

would explore both the

We could

states, so that just as

live-cat

the

and dead-cat possi-

160

/ Schrodingers Rabbits X

Translating decimal into binary

is

easy:

'

2x1.9 hundreds

tens

ones

decimal

110 110 hundred-

sixty-

thirty-

twenty-

fours

twos

sixteens

11 twos

ones

eights

fours

in binary.

For example the two sums

eights

binary

It is

also straightforward to

do arithmetic

below* are equivalent:

10 10

2

1

+

2

7

+

110 11

=

48

=

110000

numbers and

FIGURE

11-1 Binary

bilities,

the calculator

1

arithmetic.

would explore

a calculation in

which the

were in every possible combination of zeros and ones. the computer sitting in a spiall cubicle with a

human

If

digits

you imagine

operator, then

creating the impermeable barrier that separates the system

from the

outside world effectively cteates a huge array of cubicles.

shall call

this array the Dilbert Hotel,

I

with apologies both to Scott Adams, ere-

Harnessing Many-Worlds 2 / 161

to mathematicians familiar

and

ator of the excellent Dilbert cartoons,

with the Hilbert Hotel, setting for David Hilbert’s famous thought ex-

periments to

illustrate the possibilities

of

infinities.

How many

rooms has the Dilbert Hotel? Well, an 8-digit binary register can be set to 2^ = 256 possible combinations. So ff ^e are multiplying every possible 8-bit number by every other possible 8-bit number, we are performing 256 x 256 = 2^^ calculations in a hotel with 65,536 rooms. That might not sound vastly impressive, but ern computers have 32-bit or 64-bit registers.

A 32-bit

register

mod-

can be

over 4 billion different combinations. In multiplying every

set to just

number by every other 32-bit number, we generate a hotel with more than 16,000,000,000,000,000,000 (16 billion billion) rooms far more than the total number of computers ever built. This

possible 32-bit

—

is

beginning to sound promising.

However, the problem with a great deal too

like in a real office

digit,

its

is

that

leads us to expect

is

far

more mundane. Each

cubicle dif-

setting of only

one binary

immediate neighbors by the

and each worker must respond

mannequins,

in

block housing billions of computers and program-

to the

same sequence of com-

mands shouted over some public announcement are

it

own thing, following a different line of thought,

mers. Unfortunately the reality

from

image

much. You can whimsically imagine the operator

every cubicle doing his

fers

this

all

jerking about to the

same

system.

The workers

string-pulls, as if fol-

lowing the steps of a formal and intricate dance.

A more and equip

it

would be

accurate visualization

to take a single cubicle

with floors, walls, and ceilings that are perfect mirrors,

thereby creating an illusion of a vast ing off to right and

left,

different angle, so to

upward and downward. In

—each speak— but we

created something extra

number of extra cubicles

extra cubicle

is

stretch-

a sense

we have

from

a slightly

visible

certainly have not created billions

of independent worlds.

A

major practical limitation

is

that collapsing the hotel at the

end

random from the original array. Consider the task of dividing a very large number into its prime factors, a problem that arises in code breaking. You might

of the calculation leaves just one cubicle selected

naively think that one

way of using the

at

Dilbert Hotel

would be

to have

V •

«

/ Schrodinger's Rabbits

162

V

every operator try dividing a different in just his

number into

the original. Soon,

one of the vast array of cubicles a lucky Dilbert

arms over

have cracked

his head^ shouting “I

will

be waving

The remainder

it!

is

number I was given to try is the answer to the problem!” But the chance that we will just happen to get that particular cubicle when zero, the

we

collapse the system

To

negligible.

from the Dilbert Hotel, we must arrange that hold a copy of the answer that we seek. That is pos-

get a useful result

every cubicle will sible,

is

because the Dilberts are allowed to exchange information

—

to

sneak notes between one another over the cubicle walls, so to speak. But they are only allowed to pass on such information (actually by interference effects) in a synchronized

an

invisible

and

stylized way,

all

moving

to

drumbeat. Then collapsing the system by a measurement

at the right

moment

will give us a Dilbert

who

is

certain, or at least

reasonably probable, to be holding the correct answer. The Dilberts are, however, further constrained because time’s arrow must not be

allowed to operate. For the cubicles to remain in contact with one

no permanent recording of information can take place. It is to if each Dilbert is not allowed to write anything down, but merely

another, as

twist dials to

and

fro.

So commanding him to do something can

easily

scramble an already useful result that he has found.

With

all

these restrictions,

it is

almost surprising to learn that

in principle, possible to arrange the rules of the

position in every cubicle reflects the answer is

that the

method

is

task dependent;

this last

are after.

we

final

The problem

entwined with the nature of

quantum computer problem, an algorithm must be found that

the particular problem

For each different

it is

we

dance so that the

it is,

are using the

to solve.

includes

information-dissemination stage. This has turned out to be

incredibly hard.

A The

largest

Solution

in

Search of a Problem

computers have always been needed for

jobs, simulating the physical tvorld really big

programmable

purposes during World

just

two kinds of

and code breaking. Indeed, the

first

calculating machines were built for just these

War

II:

In Britain, Colossus

4

and

its

relatives at

Harnessing Many -Worlds 2 / 163

Bletchley Park cracked the

computers

at

code, while in America,

German Enigma

how

Los Alamos worked out exactly

to ignite a nuclear

explosion. Since then, computers have been turned to

Many useful

work.

tasks can

now be done on

two heavy-duty applications

for these

of code breaking, this

is

is still

id^Hy required

not available. In the case

because of the arms-race element. More-pow-

computers allow more-powerful codes to be generated

erful

and inex-

relatively tiny

pensive desktop computers, but the processing power

kinds of

all

place. In the case of physical simulations,

in the first

because of the inordi-

it is

nate complexity of the real world. Perfect simulation of anything be-

yond best

a

medium-sized molecule

we can hope

is still

beyond

The

today’s computers.

for with macroscopic systems like the weather

is

to

achieve ever better approximations. So, can

we

use a

quantum computer

to crack codes or

perform

physical simulations?

Shor’s Algorithm 20 years of searching by some of the world’s cleverest mathematicians, just one quantum algorithm fully capable of addressing a

So

far,

in

problem has been discovered.^ And even that case requires a slightly liberal definition of the term useful. The problem involves code useful

breaking.

Nowadays, we services

all

take the convenience of paying for goods

by plastic for granted. Indeed, even physical

required

—you can simply

plastic

is

and

no longer

give your credit card details over the tele-

phone, or type them into a form on a Web

site.

Yet

I

am old enough to

remember the days when almost everything had to be paid for in

cash.

Even trying to pay for groceries by check earned you a suspicious look

from the has

store manager,

come about

and often

largely because of a clever

allows an organization such as a

publish a key for sending interfered with unless

point

is

a surcharge.

it

bank or

The transformation

encoding technique that

a chain of stores to

openly

messages, which cannot be decoded or

you have a second key that

is

kept secret.

not that your credit card details are particularly secret

The

— many

people, such as waiters, have plenty of opportunity to copy them, and

164/ Schrodingers Rabbits V

it

does not take an Internet hacker. The point

details

so the recipient of such an electronic pay-

disguised.

A fraudulent debit on your credit card can

be traced to whomever

was

it

here; the important point

that I

it is

that the transaction

falsified,

cannot be

ment cannot be

is

is

paid^to.

The

details

need not concern us

that the cipher system

depends on the

fact

much easier to multiply numbers than to divide them. Thus if

give a standard

computer two

large

prime numbers

can do so in a short time. But the reverse task

which two prime numbers divide

it?

—would

to multiply,

it

—given the product,

take the

computer thou-

sands of years. The difficulty of factoring very large numbers

is

crucial

modern commercial methods. Peter Shor realized that a quantum computer could be made perform this task of factoring very large numbers. His method is

to the security of

clever that he

was awarded the

Fields Medal, then the nearest

ematical equivalent to the Nobel Prize, but the details.

The key

step

was

we

to

so

math-

are not going to go into

to link the factoring task to the

problem

of finding the period of a function. The period simply means the interval in

which the graph of a regular function repeats

functions like sine waves, the period

human

eye,

but

it

can be

is

much more

itself

For simple

immediately obvious to the

difficult to spot

discontinuous functions: Imagine a pattern

like that

with sharply

of Figure 11-2

but extending for millions of miles. Using Shor’s method, factoring a

number becomes equivalent to spotting the periodicity hidden really enormous set of random-looking numbers, and this turns

large in a

FIGURE

1

1-2

A

discontinuous function.

Harnessing Many-Worlds 2 / 165

out to be something a quantum computer can do while staying within the rules of Dilbert Space.

we could

If

would

it

build a computer to run Shor’s algorithm,

how

useful

be? Really secure messages, top-secret military and diplomatic

communications, do not depend solely on these hard-to-^ctor products of primes. The main reason is that no one has ever proved that there

is

not a clever mathematical algorithm that could enable large

be factored rapidly on a perfectly ordinary computer. The major use of the prime-number systems is to secure banking transac-

numbers

to

tions.

The only significant able

would therefore be

result

of quantum computers becoming avail-

meltdown of the developed world stretches the meaning of the word useful.

to cause a

economy. That certainly

s I

am reminded of the tension that arises in commercial companies when announces that he has discovered an interesting problem. He thinks it fascinating, but it probably represents a nightmare for everya techie

body else, who nese curse;

find

it

“May you

interesting

a real pity that

computers, because

in the sense of the ancient Chi-

live in interesting

Hope It is

more

for

no one has

—

times!”

the Future yet

found a good use

as so often in the

for

world of computing

quantum

—

it is

the

software that has turned out to be far harder to implement than the

hardware.

When

Deutsch

first

computers were pure science

worked out the ground

rules,

fiction. Since then, several

have been developed that can perform tions needed, holding nontrivial

all

quantum

techniques

the basic hardware func-

numbers of bits

in Hilbert space

—

in

other words, so that they interact only with each other without being

measured by the outside world. The most promising technology involves supercooled atoms suspended in electric fields. Other problems that Deutsch and others have solved include devising useful computer instruction sets that operate without erasing information to keep the Hilbert space together

—

essential

—and even methods of detecting

and correcting errors without prematurely reading the values that must remain hidden until the computation is complete. The latter task is

tremendously hard.

166

/ Schrodingers Rabbits

As seen from the perspective of

puter operates not on ordinary binary digits, called subtle entities called qubits. a

1,

memory location contains not a 0 or

but information^tliat can be described by a vector, an arrow point-

some point on

ing to 89.

Each

quantum combits, but on more

a single world, a

Thus

the surface of the Bloch sphere

shown on page

a qubit can be physically stored in the polarization of a

ton, or in the spin of an electron or a larger particle. But the

point about a qubit

is

that

you do not know where the vector

absence of knowledge

ing. This

is

what keeps

is

pho-

whole point-

entangled with the

it

other qubits in the computer, generating the multitude-of-Dilbertcubicles effect, space.

You

which can be thought of

are not allowed to read the qubit,

quantum no-cloning theorem

says that

cate the qubit, even without looking at

How can you environment, as qubit

s

as a little

value?

possibly

is

The

bound

tell if

to

detailed answer

is

of bits

called the

also not possible to dupli-

it is it.

interaction with the

occasionally, has corrupted the

too technical to give here, but the

analogous method for ordinary computers

Without

and something

some unwanted

happen

bubble of Hilbert

is

shown

in Figure 11-3.

either copying or reading out the values of the central square

we can

generate an extra

row and column of information

that

The corresponding technique more complicated, but has now been

enables us to correct single-bit errors. for qubits perfected.

significantly

is '

So the architecture and hardware challenges of building a quan-

tum computer

are well

for the software I

on the way to being

solved.

is

there

problem?

remain optimistic that quantum computers

wonderful

What hope

may turn out to have

uses. In the early days of the laser, there

similar dearth of useful applications.

Now

seemed

to

be a very

optoelectronic devices

based on lasers are ubiquitous in consumer gadgets, communications networks, and a host of other civilian and military applications.

quantum computers

be able to solve a very famous

hope

is

class

of problems that mathematicians

that

will

call

NP-complete. This

group of puzzles whose solution time grows exponentially

tem involved

gets larger.

problem: working out

The most famous

how

to visit a

One

is

is

a

as the sys-

the traveling salesman

group of towns with the

least

Many -Worlds 2 / 167

Harnessing

use of checksums. For example a cx>nventional computer is safeguarded by {he can generate extra digits recording whether for the square of data below, the computer is odd or even: the number of digits in each row and column

Data

in

If a bit

becomes

10 0 1 10 10 10 11

0

100

1

0

000

1

corrupt, the

0 1

checksums

for both

100 1 \^.

/ Schrodinger’s Rabbits (

FIGURE

13-1

Quantum

\

Sleeping Beauty.

You ponder. Surely the answer must be simply one-half, assuming it

was a

fair coin.

But then a curious point occurs to you.

If the

heads up, there are two occasions on which the scientist this question.

But

occasion. There

is

if

the coin

therefore a

fell tails

coin

will ask

fell

you

up, there will only be one such

good case

that the correct answer

is

two-

thirds!

The problem can be made more dramatic little.

lette

Suppose that instead of tossing a coin, the

wheel with 100 numbers on

particular

number, he

will

it.

we

if

raise the stakes a

scientist spins a rou-

He tells you that if it comes up one

wake you and put you back

times before ultimately killing you! However,

if it

to sleep 10,000

comes up any other

The Terror of Many-Worlds / 195

number, he first

will let

you go on your way unharmed

time.

You awaken.

are forced or tricked into taking the

How

sleeping

first

you and you

be allowed to walk away. But by another reckoning,

outcome stances

on the

If you

fatal

branch of the

survive, so

you

tree,

—

let

draw an

awakening-in-

and only 99 on the branches

are probably

—on awakening

me

the odds at

in

doomed.

tend toward the optimistic point of view

second experiment, you would

vival

You

will shortly

if )jou

tree like that in Figure 13-1, there are 10,000

which you

pill.

scared should you feel? By one reckoning, the chances

are 99 percent that the roulette wheel spared

this

waking the

after

feel

in

99 percent confident of sur-

introduce a slight variation that does not really change

all.

The room

independent witness

in

who

which the experiment

is

done contains an

observes every awakening of every subject

the scientist does this experiment on.

hundreds of subjects, most of

(He repeats the experiment with

whom

of course survive.) As you

awaken, you see the witness observing you with an enigmatic expression before getting

up from her chair and

leaving, because although

knows the roulette-wheel outcome, she is not allowed to give you any clue. Your blood chills as you realize that she has gotten up from her chair like this on thousands of occasions, and on 99 percent of

she

those occasions the subject before her has been doomed.

whereas before going to

sleep,

feel

The Sleeping Beauty problem, answer. But Lev

seems that

you were 99 percent confident of

on awakening you should

vival,

It

sur-

very afraid

as

Vaidman has written

it is

a

called, has

no agreed-upon

paper in which he claims that

he and Simon Saunders, two many-worlders, have a straightforward

answer to the

first

device, such as a

case

if

the coin

is

replaced by a

photon which can be absorbed or

quantum-random reflected.

^

Because

then the ignorance interpretation of probability does not apply; both

world

lines

have equal measures of existence by Everett’s rules and

hence so does each of the three episodes of awakening. awaken, what mathematicians coin

fell

call

When you

your rational expectation that the

heads up should be two-thirds. By consistency, the answer

should be the same even

if

a classical

randomizing device such as a

s

i96

>.

/ Schrodingers Rabbits

when you awaken,

coin was in fact used. Similarly^ in the second case,

your expectation that you

will survive

should be only

1

percent.

This answer to the Sleeping Beauty problem remains controver-

But the

sial.

tale is at least a

charming

classical

introduction to the

kind of philosophical Conundrums that arise in many-worlds reasoning about the

At the

self.

moment

the philosophy of many-worlds clearly contains

more questions than answers. But choices,

where does

terms of practical everyday

in

this leave the reader?

The

best

the opinions of those most knowledgeable in the ago, sitting next to

David Deutsch

at a dinner,

I

can do

I

field.

A

is

to quote

year or so

had the chance

to ask

him, “Is there

any decision that you would take differently on account

of believing that you are in a many-worlds universe, rather than in a classical

one?”

Rather

typically,

you

question, ‘Do

he smiled and answered, “Yes.

believe that

you are

I

would answer the

many-worlds universe?’

in a

differently.”

it

more serious answer, which boils would be crazy to behave in any other

in proportion to the

measure of existence of the possible

But on being pressed, he gave

down

No. He believes that

to

way than

his

worlds consequent on your actions. In every practical

life

decision,

including those involving gambling using either classical or

quantum

V

random number

generators and those that involve risk

termination of his choices in a

tum

own

quantum

thinkers

existence

whose opinions

I

expectancy

on an

I

call

island

no remaining dependents and

at stake,

they might be tempted to

half the

me

the “Krakatoa argument.” If you

is

Most quan-

Some physicists are more equivocal, com-

form of the quantum-roulette gamble. To of what

same

respect agree with him.

in their old age, with

tively little life

possible

exactly the

multiverse as in a classical universe.

But there are dissenters.

menting that

—he would make

—the

rela-

some

this is

merely a version

know

that the volcano

about to blow shortly, and your available funds are only

amount needed

to

buy

a place

on the

last

boat out, then

it is

The Terror of Many-Worlds / \ 97

perfectly reasonable to go into the casino

the red

—even

spirit, if

if

and bet

all

your money on

the odds are slightly poorer than even. In the

you reach

a point of old age

same

and infirmity where only im-

mensely costly medical and nursing care would improve your quality of life to a level where it was worthwhile to continue, the time might

come

to attempt the quantum-roulette gamble.

also argue that

by then the roulette gamble

you believe only

is

Of cour^ you could

a sensible choice even

if

in a single world.

Another advantage of postponing your decision for as long as possible is that,

by then,

physicists

and philosophers may have revised

And there is the possibilpossibility we ity that we live in a multiverse of finitely many worlds, a

their advice.

Many- worlds

is

not yet proven.

That makes a fundamental difference to quantum Russian roulette and similar games. Infinity divided by 100 million is exactly the same infinity as before. But a merely very

will consider in the last chapter.

large

number divided by 100

million

is

that

many

times smaller, for

example, lO^^o divided by 100 million shrinks to 10^^ killing the overwhelming majority of potential future yous. Personally, I will be sticking with Deutsch’s advice.

— CHAPTER

14

%

THE CLASSICAL

WARRIOR

Roger Penrose

V

B hat if quantum theory

^

is

.W

bring about

some

is,

after

The principle

first

incomplete? What

as-yet- undiscovered physical

quantum

collapse,

mines the case for many- worlds? This a possibility that

all,

some

physicists

still

is

mechanism

if there

that can

and by implication under-

now a minority view, but it is

take seriously.

reasonably watertight specification for such a collapse

was formulated

in the 1980s

Ghiradi, Rimini, and Weber

—following

by three a

Italian physicists

program suggested by Philip

Pearle. In their honor, specific physical collapse

mechanisms postu-

GRW-based mechanisms. Their basic point was very simple. Systems in which quantum behavior had at that point been observed involved very small numbers of lated ever since tend to be referred to as

fundamental

particles,

most

typically

one

(as in the two-slit experi-

ments that had been performed by that point), or hundred. Suppose that there

quantum wave function

at

is

some mechanism

random

object described by a spread-out

intervals

—so

in such a

way that

most

just a

few

that collapses the

that, for

example, an

wave function suddenly pops back

into existence in a single well-defined place

works

at

—but the mechanism

indithdual particles are collapsed only at very

198 •%

The

Classical Warrior:

Roger Penrose / 199

long intervals, yet systems containing htige numbers of such particles are collapsed at very short ones.

An appropriate collapse probability might be on the order of 10“^^ per particle per second. Obviously, the chance of a particle collapsing into a single position in the tiny fraction of a second during

which

it

through a two-slit experiment (or any other experiment done on a human timescale) is utterly negligible, so wavelike behavior is observed. On the other hand, anything large enough to be considered as

flies

a classical

measuring device

laboratory instrument

observer, be

it

lapse to a single location

human, or lO^'^

a

to

such a system would be expected to col-

and

state in a tiny fraction

of a microsecond.

GRW put forward their program, several people have suggested

specific candidates for

such a collapse mechanism.

The most prominent of them

is

Professor Sir Roger Penrose, and

his ideas deserve special consideration because

able

a cat, a

—contains something on the order of

10^^ particles. Accordingly,

Since

—an

he has done consider-

work devising experiments which could actively verify them. Now

in his mid-70s,

Penrose

is

one of those

scientists

who

has remained

remarkably undiminished by age; in both mental and physical agility, he could easily pass for a man in his 50s. In many ways he is the last

and most impressive representative of the old school of quantum thought. He epitomizes it especially well because on the one hand, he is

seeking a very specific and reductionist physical

mechanism

to ex-

quantum collapse; yet on the other, he assigns at least as much importance to more philosophical issues, and specifically to the possibility of a link between quantum and the nature of human consciousness. To me, and perhaps to others who embrace the new school of

plain

thought, this

is

both

slightly paradoxical

attitudes of such past figures as

Penrose

is

now

retired

and

eerily reminiscent

of the

von Neumann and Rohm.

from

his distinguished post as

Professor of Applied Mathematics at Oxford University.

Rouse

The

Ball

achieve-

ments that first raised him to worldwide prominence date to the 1970s. Their common link is geometry, because his ability at mathematics is

combined with extraordinary

visual insight. At the recreational level,

he has invented paradoxical shapes of the type made famous by Escher. His discovery of ways to tile a plane in a pattern that is nonrecurring,

200 / Schrodingers Rabbits

infinitely varied,

and not predictable by any computer algorithm

beautiful illustration of a deep his

work on matrices

warped

problem

in

descried by general

ways

in

quantum theory. And I am just old enough when he and Stephen Hawking first revealed

on the nature of black

which the might be

relativity

reconciled with

ber the furor

rememtheir work to

holes.

These achievements were a third of a century ago. Yet Penrose

day this

is

more famous even than he was

when he was due

amply

large

enough

advance to find

it

a

mathematics. In physics,

called twistors has suggested

fabric of spacTe-time

is

then.

had a recent reminder of

I

to give a talk in a lecture hall that

for the seminars held there.

full to

bursting.

but the entrances, stairways,

aisles,

to-

I

is

usually

turned up well in

Not only was every

seat occupied,

and even the platform

at the front

were packed solid with young students willing to stand or crouch in uncomfortable positions for the privilege of hearing him speak.

would have been quite impossible room, and we

all

had

It

for Penrose himself to get into the

to trek across

town

to a

much

larger lecture

theatre before the talk could go ahead.

Most of that audience had not been born when Penrose made the discoveries for which history will remember him. The work that has brought him back into the public eye

many

topic. Like

on

a significantly different

physicists, in his later years

he has become increas-

ingly interested in

more

is

philosophical issues, questions that are hard

not merely to answer but even to formulate. This

him

to

new

focus has led

propose not one, but two, controversial hypotheses concerning

quantum

theory,

which have led him into

significant conflict with his

colleagues even as they have raised his profile with the wider public.

There

is

now a significant rift, which has cultural as well as ideological

dimensions, between him and the newer generation of physicists.His

views on foundational issues, the bedrock on which physics grounded,

differ

many younger scientists. I name in a discussion on the

profoundly from those of

once dared to bring up David Deutsch’s

philosophy of mathematics, to be told sharply: “David and disagree

on

just

is

I

seem

to

about every conceivable point.”

But Penrose’s enduring creativity and mental sharpness are not in doubt. The willingness to formulate

new

hypotheses, to challenge es-

The

Classical Warrior:

Roger Penrose / 201

wisdom wherever puzzles rerhain, is essential to scientific progress. With respect to quantum physics, Penrose is in the rare posi-

tablished

which

tion of having been active through both the major epochs in

quantum

interpretations were generated. Earlier in his career he

Bohm when

David

yet he has

knew

they both worked at Birkbeck Collegfe^fn London,

remained active and innovative right through to the present

day. His views certainly deserve a hearing,

and

in this chapter

examine both of his major hypotheses with respect

to

we

will

quantum.

Collapse by Gravity Penrose has gone looking for a plausible mechanism that might cause

by GRW, and found an answer suggested by a well-known dichotomy between quantum theory and gen-

collapse along the lines suggested

eral relativity.

It is

known

that

if

general relativistic effects (broadly

speaking, gravity) were subject to that other fields

and energies

are,

quantum

fluctuations in the

mathematical

A quantum

would

arise.

violently un-

would be

In physical terms, the structure of space-time stable.

infinities

way

fluctuation in a tiny region of space-time

would

very rapidly grow, perhaps spawning exotic entities, such as black holes or wormholes, at a colossal rate. so

we know that at least some

Penrose has tried to

fix

We do not observe anything like this,

correction

is

required to current theory.

two problems with one solution by suggesting

that such uncertainties in gravitational field energy tend to cancel

themselves out, producing the process

we

call

quantum

collapse as a

side effect.

Gravitational attraction, in the

modern

Einsteinian picture,

caused by a warping of space-time. In a well-known analogy,

be crudely visualized as

heavy

ball

is

balls placed

placed on

jects,

fall

can

bending of a rubber sheet when a

The heavy ball makes

on the sheet tend

small objects tend to

we normally

it.

like the

this

is

to roll

down

a dimple,

and smaller

into the dimple just as

toward the surface of a planet. Even though

think of gravitational pull as associated with large ob-

such as Earth or another planet, in

tational effects. Even gravitationally,

fact all

two atomic nuclei

matter produces graviattract

and therefore produce tiny dimples

one another

in space-time.

202

If cists,

you

reject the

/ Schrodingers Rabbits

guide-wave hypothesis

(as

most modern physi-

including Penrose, do), then an object whose position has ac-

quired a wavelike uncertainty really can be thought of as being in two or

more

places at'once. ^ut what, about

field? If the object in

does Ic,

it

Figure 14-1 could be in either of two positions,

or what?

^

14-1 (a) Space curves as

Space curves as

if

only one version of the ball

the mass of the ball

(say,

the

left

is

at the

midpoint of

its

one)

two possible

'

positions.

Space curves as

if

^

has real mass.

(c)

associated gravitational

curve space-time as in Figure 14- la. Figure 14- lb. Figure 14-

FIGURE (b)

its

if

there are

two versions of the

ball,

each with real mass.

The

Classical Warrior:

Roger Penrose / 203

Penrose’s hypothesis can be expressed in terms of the picture of

Figure 14- Ic, where space-time starts to be deformed as ferent objects. Like

an

elastic

if

by two

dif-

band being stretched, this kind of double

dimple stores energy. Penrose suggests that the fabric of space-time resists this

kind of thing, and that the higher the energy stored in the

double dimple, the more

likely

quantum

collapse

is

to

pop the

object

into a well-defined location.

How cause

He

great an uncertainty in the gravitational field

quantum

collapse?

Here Penrose

resorts to

is

needed

to

an admitted guess.

speculates that the collapse time, T, in an isolated system (that

is,

one that

is

not currently interacting with or being observed by a larger

system)

is

of the order h/2nE, where h

we met

quantity

in

Chapter

leased by allowing the

2,

and E

is

Planck’s constant, the tiny

is

the energy that

two versions of the object

to

fall

would be to their

re-

com-

mon center of gravity. For everyday masses time, Ty

more

—

—the expected

collapse

billiard balls, say

would of course be very short indeed. However,

significant for tiny objects,

it

becomes

and Penrose has calculated the

fol-

lowing approximate collapse times: Beryllium ion ~ 100 years

Water drop 2-\xm diameter

(just visible in

microscope) ~

1/20 second

Cat ~

10“^^

second

You may find

it

interesting to

compare these with the collapse-by-

decoherence times given in Table 7-1.

There are hand-waving elements to Penrose’s argument, but one very important thing sets

him ahead of

others

who

have proposed

GRW-type collapse mechanisms. He has been brave enough to propose a method of testing his theory, and put considerable effort into refining

very to

it

first

toward

practicality.

By chance

I

was privileged

to hear his

public description of the suggested experiment in a lecture

Oxford students, the day before he gave

tion at Imperial College in

it

a

more formal

presenta-

London.

The proposed apparatus

is

our old friend the Mach-Zender

inter-

/ Schrodinger’s Rabbits

204

\

ferometer, which

we met being used as a bomb

illustrated in Figure 10-

the photons requires that

all

detector in Chapter 10,

Wavelike behavior in this device ensures that

1.

arrive at detector E. Wavelike behavior of course

we do

rqake

liot

an]^,

measurement of which of the

two possible routes the photon takes through the main part of the apparatus.

Suppose we replace the fixed mirror

move?

It

will

tiny that

at

B with

now recoil slowly if the photon hits

under normal circumstances

uncertainties in the mirror’s position

it

will

it,

one- that

is

free to

but the effect

is

so

be swamped by other

and motion, so no interference-

destroying “measurement” will take place.

But what

if

we make

the distances

order of thousands of kilometers?

move

Then

a significant distance while the

Penrose’s theory

is

BD

and

AC very large

—on the

the mirror will have time to

photon

is still

in flight. In fact, if

correct, the uncertainty in the mirror’s position

caused by the lack of definiteness as to whether the photon went via mirror B or by the alternative route becomes so large that gravitationally

induced collapse occurs. The mirror “pops” into one position or

the other. At that the other. like

When

moment

it

the photon gets localized

arrives at the detectors,

it

will

on one route or

behave in a particle-

way, with an equal chance of being detected at E or at

differs

F.

This

from the predictions of orthodox quantum theory.

This would be a very difficult experiment to do. The only practicable

way

mount

to get the long

photon path lengths required would be

the experiment aboard a pair of

satellites,

to

which would of

course be very expensive. Penrose speculated on ways to get around this

problem.

One possibility would be to

photon, whose energy and photon. Unfortunately,

it is

momentum also

is

use an X-ray or

much

much more

gamma-ray

higher than a visible

difficult to generate

and

handle such photons. For several years, Penrose (whose retirement has been more nominal that actual)

worked with Oxford graduate student William

Marshall and others on ways to possibility Marshall told

me

make the experiment practicable. One

they were exploring involved bouncing

the photon repeatedly between two closely spaced mirrors

on each

leg

of the apparatus. Using mirrors tuned to the relevant wavelength to

The

create to

what

called a high-finesse cavfty, the

is

photon could be made

bounce millions of times before continuing on

have two benefits. The

photon

is

its

way. This

would

to increase the delay time before the

first is

to a reasonable value while keeping the apparatus

measured

The second

quite compact. is

Roger Penrose / 205

Classical Warrior:

is

one of the cavity mirrors,

that

it

if

the mirror that

will get kicked

is

move

allowed to

not once by the photon,

but a huge number of times. (Think of a tennis

ball

bouncing rapidly

between your racket and the ground when you hold your racket close to the ground.) fect

on the position of the mirror than

the mirror

made

is

mounted on

to vibrate to

in theory cause it

The repeated photon bounces have

it

and

much

bigger ef-

would

a single reflection

do. If

a flexible support, a silicon cantilever,

fro to start with, the effect of the

end up

to

a

and

photon could

in a significantly different position to that

would otherwise have occupied,

opposite end of its swing. By

at the

Penrose’s argument, the mirror will spontaneously collapse itself into

one of those two positions, thereby determining ity

the photon

is

in

and abolishing interference and Marshall published

In 2002, Penrose

more

definitely

which cav-

effects.

a

paper describing

this

sophisticated version of the experiment.^ However, the authors’

own calculations show that using off-the-shelf technology, it would be about 100,000 times

less sensitive

than required to prove Penrose’s

hypothesis. Definitive results will not be

coming anytime soon.

In the absence of experimental proof, establishment’s verdict said that

it is

on Penrose’s

fairly dismissive.

many when he

a

the current

gravitational collapse?

It

has to be

Stephen Hawking probably speaks for

new physics,

that

it

perfluous to look for alternative mechanisms.

might be

is

says that decoherence explains collapse so well, with-

out needing to invoke any

this

what

has simply

My own

become

feeling

is

su-

that

harsh. At the very least, Penrose’s highlighting of

little

the fact that different

quantum outcomes can

rapidly lead to

presumed

outcome worlds where the very shape of spacedifferent is worthy of further pondering, and ex-

interference between

time

is

significantly

perimental investigation

The bottom

line,

if

possible.

however,

is

that Penrose’s collapse

mechanism

does not resolve what we have identified as the one true dilemma of

quantum

theory: the nonlocal nature of collapse. Penrose agrees that

— 206 / Schrodingers Rabbits K

if

we were

to entangle

two systems and move them a light-year apart,

collapsing one of the systems

—by observation or by

—would

gravity

instantaneously change the expected results of a hieasurement on the

second system.

It

woul'li seecn that

ypu could send a “forbidden” faster-

than-light message in this way; by fiddling with the mass that triggers

quantum collapse, you could select which of the two distant detectors the photon would arrive in, right up to the last moment. This does not necessarily cause paradox, however. The backwardin-time signaling we discussed in Chapter 4 depended on the fact that the

we had two

pairs of faster-than-light signalers in

two

different frames

of reference, aboard trains moving in different directions. There are still

a few physicists

who hope that, special relativity notwithstanding,

the universe will turn out to have one preferred stationary frame of reference after

all,

violating the principle called Lorentz invariance

that the laws of physics look the velocity. If there

same

to all particles,

whatever their

were such a unique frame of reference, then

faster-

than-light information transmission with respect to that frame only

would not equate paradoxes.

to backward-in-time signaling,

One such model was formulated

and would not cause in

1949 by

Howard

Robertson of the California Institute of Technology, and developed further in the 1970s by Reza sity

Mansouri and Roman

Sexl of the Univer-

of Vienna. As recently as 1998, a set of Loren tz-violating interac-

tions

was postulated by Sidney Coleman and Sheldon Glashow

at

Harvard University. But no evidence for Lorentz violation has ever been discovered, and conventional the overwhelmingly

relativity remains, to

put

it

mildly,

more accepted paradigm.

Penrose’s genius notwithstanding, his fondness for his gravitational-collapse hypothesis might, at the that

most of

others,

his life

was

end of the

day, reflect the fact

lived before the experiments of Aspect

which have unequivocally proved that nonlocality

fore nonlocality

is real.

and Be-

was proven, finding a plausible collapse-causing

mechanism was perhaps the most urgent problem of quantum theory. But now nonlocality must be faced, and no local collapse mechanism, however

cleverly devised, can» appease

its

dragons.

The

Classical Warrior:

Roger Penrose / 207

Collapse inlVIind much

Penrose’s second hypothesis about

quantum

more

ironic that thanks to his popular

speculative than the

first. It is

books, in particular The EmperoPs

New

collapse

Mind,^

it

is

is

very

by^ar the best

known of his ideas to the general public. In an earlier chapter, we mentioned the dubious hypothesis that conscious observers play a special

we discussed the likely manufacture of quantum computers in the near future. Somewhere between role in the establishment of reality. Later,

and

these two poles of wild

solid speculation

comes Penrose’s notion

human mind might itself be a quantum computer. His demotive is to explain how our minds can have certain capabili-

that the

clared

ties that

he claims would be impossible for any computer operating

according to the principles of classical physics.

The is

a

vast majority of scientists today accept that the

form of computer. Of course

top in

it

differs

human brain

from the one on your desk-

many ways. The most striking is that your computer has a single

processing unit that

is

doing just one thing

your brain consists of some 100 each acting

from up

like

and then broadcasts

its

neurons

own

neurons

all

operating at once,

it is

hooked up

to

electrical signals

on the input

signal to a different batch of

side,

neurons on

Some neurons connect to locations outside your brain,

for example, receiving signals telling

any one time, whereas

an independent computer that reads

to 10,000 other

the output side.

billion

at

from the

retinal cells in

muscles to contract. Thus your brain

is

your

eye, or

also able to interact

with the external world.

But does the power of 100 billion processors make your brain fundamentally different from a desktop computer? The answer turns out to

be no.

One

of the foundations of

modern computer

theory, in-

vented by the British mathematician Turing during the Second World

War,

is

that any

cal physics,

computer that operates according to the laws of classi-

massively parallel or otherwise, can be exactly simulated

by a very basic computer capable of executing just one simple instruction at a time, provided

you

give

it

enough time and enough memory

with which to work. Such a machine can be

—and has been—

from

can in principle exactly

a simple construction toy like Lego, yet

it

built

/ Schrodingers Rabbits

208

simulate the workings of any computer based on traditional physics,

from your desktop If

you accept

PC

to

your brain works by

that

only difference between

ming.

We

already

an organic brain.

it

and youi^desktop PC

know how

to

then the

classical physics,

program an

is

scale

and program-

electronic

computer

to

simulate the workings of a small group of neurons performing a

simple task, but to simulate the

human

quire at least 10^^ binary digits of

desktop probably has a

program still

—

it

appropriately.

thankfully, for

But Penrose

The

an

the order of 10^ binary digits,

insect,

even

if

task of replicating the

moral reasons

feels

memory. The computer on your

memory size on

insufficient to simulate the brain of

brain a computer would re-

—way beyond

we knew how to

human

brain

us.

human and programming. He

strongly that the difference between the

more than mere scale believes that human intuition, or more precisely what he regards the ability of our minds to transcend algorithmic reasoning (that brain and a computer

is

step-by-step reasoning using a fixed set of rules) proves that there

be some beyond-Turing-machine aspect to our minds. in particular the “aha”

problem

in

is

moment when we

He

as is,

must

describes

have been worrying

at

some

an unimaginative step-by-step way without making any

progress, then suddenly a lateral-thinking

by seeing things

in a

new

method of going forward,

way, seems to pop into our heads without

warning. To him, this seemingly instant condensation of nebulous thoughts into a coherent solution

is

strongly reminiscent of

quantum

collapse.

Penrose highlights one example that he arises

feels

proves his point.

It

from an attempt 100 years ago by the remarkable mathemati-

cian Hilbert (whose Hilbert space and Hilbert hotel

we have

already

met) to formulate a mathematical language with a comprehensive

set

of axioms and rules that, within the context of a given mathematical system, will allow any proposition ingful statement false.

—

to

—

that

is,

any grammatically mean-

be explicitly demonstrated to be either true or

Because such a language contains a

finite

number of symbols,

number of statements of given maximum length that can be made. Because there are also a finite number of rules for manipulating the symbols, an appropriately programmed computer there

is

a finite

The

Classical Warrior:

Roger Penrose / 209

could easily fiddle about with the axioms to deduce further true

ments from them

was given

until

it

entirely mechanical process.

becomes an

it

computer could

versely, the it

—

was

fiddle

state-

Con-

about with any arbitrary statement

either reduced to

some combination of

the

axioms, or shown to contradict one or more of them.

However, a perfect system of this kind, can be proved true or

false

in

which every proposition

by applying such a sequence of steps, turned

out to be very elusive. Finally a mathematician called Godel discov-

Any such system must

ered a remarkable thing.

necessarily contain

that are in fact true, but that can never be proved

some statements

within the rules of the system. The essence of his proof was to the possible propositions that can be made, and rectly

all

list all

the possible cor-

formulated proofs, in a kind of alphabetical order, demonstrat-

ing that

some of the proofs we might expect

to find will inevitably be

missing.

Penrose claims that a Turing-machine type of artificial intelligence

would find

it

impossible to understand

able statement

terms of the

what he

is

might

rules.

driving

in fact

at.

a lifetime.

such a Godel-undecid-

be true, despite lacking a formal proof in

Other people, myself included, cannot

really see

What do we mean by “true”? Each of us

intuitive definition, arising

ment of

how

from the experience and mental develop-

When we

the kind described above,

has an

are given a mathematical rule system of

we can temporarily

accept a redefinition of

truth as “provable by manipulating the symbols according to certain

we have not really forgotten our broader and when we find the rule system inadequate, we ap-

specified rules.” But of course

notion of truth,

peal to that broader intuition.

Penrose might well be right in his feeling that a

ment of intuition

represents a collapse of multiple tentative threads of

thought into a single successful perception. And

gous to what happens when the

tum computer

parallel

noted

why

the brain

at the start

neurons

is

is

this

is

certainly analo-

“thought processes” of a quan-

collapse into a single

computation. But of course there explain

human “aha” mo-

outcome

no need

at the

to invoke

end of the

quantum

capable of massively parallel processing.

to

We

of this section that the brain has a hundred billion

at its disposal.

Of course our

brains use parallel processing.

y

2i0 / Schrbdingers Rabbits \

and no doubt our apparent thread of consciousness

is

a retrospec-

tively

constructed story in which the work of unsuccessful subnet-

works

is

jettisoned,

networks

—

this

and we remember only the reports of the successful

among

rapidlys.becoming the consensus view

is

neuropsychologists.

Godel’s theorem

a fascinating mathematical result with real

is

might be many reason-

practical implications, in particular that there

able-sounding problems that a conventionally programmed computer

would require an

infinite

time to

solve.^ Penrose’s

appeal to

quantum

seems to be based on the hope that some kind of ultra clever quantum collapse

might give our minds

infinity solutions.

puters,

we

But when we come to study

see that they

outperform

rather than qualitatively.

but

it is

never

flashes of intuition

infinite.

classical

The advantage can

about those beyond-

quantum com-

real

ones only quantitatively

potentially be impressive,

Penrose himself seems to acknowledge that to

return information about results that could not be found in finite time

by a Turing-machine computer, quantum collapse would have sess properties additional to

known to have. What has made the public,

and even weirder than those

to pos-

already

it is

quantum consciousness so popular with him to work on it for so long? Probably it is

Penrose’s

and inspired

the enduring longing to believe that the physical basis, as distinct from the

mere software, of human beings

dane material world. Once,

dowed with some animal and then

all

in

living

some way transcends our munthings were assumed to be en-

special vital force.

human

cadavers, the

As experiments probed

body was seen

somewhere were

still

in the brain.

Around

the time

I

mere inge-

to be

nious machinery. The physical mystery retreated toward a

last

hideout

was born, some doctors

trying to weigh bodies at the point of death, attempting to

detect a small reduction in the weight as the soul departed. find a tiny reduction following the last breath.

ancy of the body-temperature

I

suspect

a wonderful thing, but

it

it

(They did

was the buoy-

air in the lungs, lifting the

hot-air balloon with a force of a fraction of a gram.) is

first

body

The human mind

ne^ds no unique physics to explain

4

like a

it.

CHAPTEG

THE

NEW AGE WARRIOR Anton

rists

Zeilinger

What do you call a physicist who works on quantum theory? Why, a quantum mechanic, of course! The joke is funny (at least to physicists) because most quantum theohere

T

15

is

a hoary old joke:

are just about as far

possible to get.

from being

They tend

to live in

practical, applied types as

it is

mathematics or philosophy de-

partments rather than physics buildings, regard running a computer simulation as getting their hands dirty, and probably have not been in

an honest-to-goodness laboratory since their undergraduate days. You simply cannot imagine them doing the kind of physics experiment that involves spanners

and

grease.

By these standards, Anton Zeilinger

is

indeed a quantum me-

chanic. His excellent physical intuition has enabled

of the most dramatic experiments to date to

quantum mechanics. For example, two-slit

it

test the

was he who

to devise

some

foundations of

first

upgraded the

—which caused such excitement when was electrons rather than photons — to work with

experiment

performed with

him

it

first

buckyballs, giant molecular cages comprising 60 carbon atoms. Even these football-like structures, each with a definite rigid shape

and con-

taining hundreds of fundamental particles, can be demonstrated to be

211

212 / Schrodingers Rabbits X

two places

“in

at

once”

—or

at the

very

exploring two paths at

least,

once.

^

When

I

first

met him,

Zeilinger

was perfecting a

larger-scale ver-

sion of the Aspect'experiment, in\which the photon paths could be

extended up to several kilometers.

He was determined

to

several potential criticisms of the original Aspect setup. His

was

to ensure that the choice of polarization

photon was truly random, because

in Aspect’s

overcome

main

measufement

goal

for each

experiments the mea-

surement direction was selected using acoustically driven optical switches that flipped at regular (albeit very fast) intervals, so

it

was, in

principle, predictable in advance.

After describing his

new experimental

design to a colloquium at

Oxford, Zeilinger asked the audience to suggest better ways to make the

measurement directions

at

each end of the experiment completely

independent and unpredictable. For example, you could use tables of

random numbers generated might be better

still

in

advance to

it

them only at the very last moment when using a real-time random-number genera-

to decide

the photons were in flight,

tor of a type developed for cryptography.

gested was that two

but

set the directions;

Another

alternative sug-

human observers, each armed with a toggle switch,

could consciously decide the direction of each measurement as suited their all

whim. Of course

these ideas,

the physics

I

am sure that Zeilinger had already thought of

and more,

for himself.

community was

to

make

The purpose of

sure that after the experiment

was done no one could turn round and

ment choices were not ” have done is this

sufficiently

Most experimenters who are

hoping that sooner or

pected. After

all,

say,

“Ah, but your measure-

random. What you should

test the

later

his canvassing

really

foundations of quantum theory

they will turn up something unex-

for confirming a well-accepted physical theory to

extra decimal place, an experimenter can expect at

—

most

a pat

an

on the

new for example, something that throws new light on the elusive quantum collapse process that brings the chance of greater rewards. At a dinner when I had the chance to

back.

It is

discovering something

question Zeilinger in

morq

depth,

it

—

became

expect the unexpected to turn up at any point

clear that

—he

he does not

believes the ortho-

The

New Age

Warrior: Anton Zeilinger

/ 213

#

doxy will be confirmed every time. As we talked, I became increasingly puzzled as to the motive for his admittedly beautiful experiments. Eventually

asked, “Are

I

you trying simply to rub the theorists’ noses

the fact that the problems of

quantum theory

are real,

in

and cannot be

ignored as they are demonstrated at ever larger scales1”^e beamed

and

replied, “Yes, that

He

so. Exactly!”

has continued to enjoy tweaking the theorists’ noses. For ex-

ample, he designed a

ment

is

new version of the buckyball interference experi-

work with hot

to

buckyballs, ones at such a high temperature

that they emit several infrared photons slit

device.

He

asked various theoreticians whether they expected an

interference pattern to be produced.

on the

basis that the infrared

ment would

on the way through the two-

constitute

They predicted

that

it

would

not,

photons striking the walls of the experi-

“measurement”

—an

irreversible interaction

with the environment that would destroy interference. But Zeilinger predicted that he would get an interference pattern after

all,

because

the wavelength of the infrared light emitted by the buckyballs was so

long that

did not convey sufficiently accurate information about

it

their position to tell the

through.

And

When

I

environment which

slit

they were going

of course he was right.

first

asked Zeilinger which interpretation of

quantum

theory he favored, he was reluctant to reply. Eventually he said, “I think there

is

a

need for something completely new. Something that

different, too

“Some would be

unexpected, to be accepted as

variant of many-worlds?”

yes.

He brought

his

I

too

yet.”

asked, expecting the answer

hand down on the

and gave a monstrous Teutonic “No,

I

is

table with a

thump

snort.

do not think many-worlds

is

right at

all.

Absolutely not!”

And he would not be drawn further. But now, several years later, he has come clean; he does indeed have a radical suggestion, which is new in essence

and certainly deserves

to

be taken

seriously.

His view

is

based on one of the most fundamental differences between a universe

made up of quantum systems, and one that is classically continuous: A quantum system can contain only a limited amount of information.

2i4

/ Schrodingers Rabbits y,

Continuous The

difference

Is

Infinite

rather neatly illustrated by a

is

humorous

science

fic-

mahy years ago by Martin Gardner. In the story, an on Earth and offers the human race the entire sum of his

tion story written alien lands

incredibly advanced race’s knowledge, 'helpfully translated into English. (Apparently

who

Gardner gets a lot of correspondence from people

claim to have had an alien land in their backyard

similar offer.

He

The from

unsolved by humans.

far

He

alien’s offer is gratefully accepted.

his spaceship. “This

length to

numbers

its

spell

known to be soluble,

never hears back.)

He produces

a glass rod

rod encodes the entire contents of the

brary of Zaarthul,” he says. “All you have to do its

a

writes back, politely asking the alien to give the an-

swer to any one of several mathematical problems

although so

who makes

width with an accuracy of

is

measure the

ratio of

billion decimal places.

1

Li-

The

out an English translation in a simple two-digit code

where 01 stands

for A, 26 for Z,

and so

on.”

Then he

seals

up

his saucer

The human scientists try to measure the length and width of the rod as best they can, but they never get beyond the first few and

flies off.

of the message.

letters

Gardner was jesting, of course, because cal objects are

made up

would be about width

ratio

mation

at

10^

glass rods

of the quantized units

atoms wide by

10^

we

and other physi-

call

atoms. The rod

atoms long, and so

its

length/

could encode some eight or nine decimal digits of infor-

most. However,

if

we

lived in a universe

where objects were

made of a continuous substance that could be subdivided indefinitely, it would be possible in principle to make Gardner’s rod. In fact if we lived in a nonquantum universe, it would be positively wasteful for the alien to use such a large physical object.

Consider the

of an electron as a tiny spinning top, with in a specific direction.

shown

in Figure 15-1.

particle says.

The

alien

its

axis of rotation pointing

need hand over only one electron,

“Measure the angle between the spin

and Galactic North, accurate to one billion decimal

(Of course “Galactic Ngrth” would need

fined,

classical picture

as

axis of this places,”

he

to be very precisely de-

perhaps with respect to a master compass consisting of another

electron.)

However,

'

in reality, electron spin

is

a

quantum

property.

The only

The New Age Warrior: Anton Zeilinger / 215

measurement we can make

is

whether the spin

is

up or down

relative

an arbitrarily chosen plane. This yes/no answer can yield only a

to

single bit of information alien’s

and

so, in

our universe

encoding scheme would be not

this

refinement of the

just technologically difficult,

but fundamentally impossible.^ Indeed, modern theory implies that there

is

an upper bound on the amount of information that any object

or system can contain. For a macroscopic object like a glass rod,

becomes very finite

just it

it

large but certainly not infinite. Correspondingly, only a

amount of information

is

required to describe a given object not

—

approximately but perfectly

to record

all

the information about

that the universe contains.

This has profound implications for physics. The whole universe

we

perceive contains only a limited

amount of information.

It

could

be described completely by a sufficiently long string of zeros and ones.

Our world might

therefore be indistinguishable from a digital

com-

puter simulation of itself, just as hypothesized in countless science

fic-

tion stories. This contrasts completely with a classical, continuous

universe for which the simulating computer would have to record an infinite

number of

and spin of a

single

digits just to specify the exact position, velocity,

fundamental

particle.

216 / Schrodingers Rabbits %

A

picture in which information

is

underpins the thinking of physicists

at

both

and conserved now

finite

every scal^, from string theory

to cosmology. For example, the property of black holes that physicists

nowadays find most puzzling

is

capacity to swallow matter

ncft their

(which can eventually escape as Hawking radiation), but their apparent ability to permanently swallow information.

The Information This information-based view of physics

new

Zeilinger’s is

insight?

It is

is

now decades old, so what is

so simple that

often the case. But to understand

it,

it

took a genius to see

we must

first

it,

as

think rather hard

about what we mean by information. In information theory, the basic unit of information

something that can have either of two values. In

computer, one

a

represented by a microscopic switch that can be either on or ever, a bit, or a

some

bit

is

it is

on quantum computing. But the same

ters,

a' letter

in the standard alphabet

or the color of a pixel to be displayed

of a musical note to be played, or

computer the

is

concerned, a bit

human programmer

what he

is

trying to

is

we saw

How-

it

false.

A

in the

For a set

of

chap-

of digits could also be

set

used to display text characscreen, or the timbre

on the

many

other things. As far as the

just a bit, a switch that

can use

make

true or

as a binary digit.

binary digits can represent an integer number, as

denoting

is

denoting the truth

bit as

proposition, recording whether

mathematician, the normal use of a

ter

off.

bit

sequence of bits, can be interpreted in different ways.

For example, a logician tends to think of a value of

the bit;

is

A

understand what a program

on or

off.

But

ways depending on

in different

the computer do.

is

rival

computer pro-

doing by looking

at

grammer, trying

to

the binary bits

generates, will not get very far until he can interpret

it

what kind of information though the computer fectly well

without

itself

this

is

is

being represented by each bit

could not care

less

—even

and can function

per-

knowledge.

we view the universe as a sort of giant computer manipulating a but finite number of t>its, there is still the question of how to

If

large

interpret the information the universe-computer

is

storing

and pro-

The New Age Warrior: Anton Zeilinger / 217

cessing.

The most natural assumption

is

relates to a particular point in space-time.

computer models of physical systems ference

is

that each bit of information

This

like the

that whereas weather simulations

is

very like the

way that

weather work. The

dif-

on present-day computers

have to divide the atmosphere into imaginary cubes measuring kilometers on each

side, a true

universe-simulation would hold informa-

tion at a vastly finer scale, of the order of a Planck length.^ Zeilinger’s

approach

is

radically different.

a given bit of information held

He prefers to

think that

by the universe-computer can be

preted, not as information about

what

is

going on

at a specific

inter-

point of

the space-time continuum, but as the logical value (true or false) of

made about quantum systems. This interpretafact that a quantum system considered as a whole

statements that can be tion allows for the

can contain information that

is

not present in

its

constituent parts.

Nonlocal Information Figures 15-2 and 15-3 illustrate the principle of distributed information.

FIGURE

15-2

An

entirely

random

pattern.

218

examine

If you

/ Schrodingers Rabbits

either picture

on

its

merely look random to the unaided eye,

own, the dot pattern does not it

really

is

arbitrary,

and even

the best code-breaking machines at the National Security

could not extract any meaningful information from

up

the page

to a bright light,

you

it.

will see a very clear

ous pattern, which of course you are

Yet

if

Agency

you hold

and unambigu-

free to interpret as the figure “0,”

or the Eye of God looking at you, as you please.^

How

is

this possible?

We

will illustrate

with an anecdote. Let us

suppose that you are the general in charge of a besieged

want

to

send a message to your king

telling

castle.

You

him how many days you

can hold out before you will have to surrender

if

help does not arrive.

number of brave volunteers prepared to sneak out at night and try to make it through the enemy lines, which is fortunate because

You have

a

radio has not been invented yet. However, there

know that

if

because the

the messenger

enemy

is

will discover exactly

15-3 Another entirely

a

dilemma. You

intercepted, the result will be disastrous

order to achieve victory.

FIGURE

is

random

pattern.

how

long

it

has to wait in

The

New Age

Then you have but

if

two

Warrior: Anton Zeilinger

a brainwave.

/ 219

One messenger might be

out in opposite directions, the chance that they will both

set

be captured and forced to divulge their information

is

small.

divide the message crudely, for example, so that one

note saying “One hundred” and the other “and very satisfactory. You really need a

each note on

own

its

and

way

that

is

we need

man

carries a

to divide the

is

not

message so that

useful information at

all,

yet

both

meaning.

full

parchment.

You could

sixteen,”"btft that

the castle mathemagician approaches

a piece of

problem

no

carries

taken together convey the

Then

intercepted,

“Sire,”

he

you bearing

a stylus

have a way. The essential

says, “I

send the king an 8-digit binary number,

to

namely 01 1 10100” “Quite

so,”

you

being rather advanced in binary math by the

say,

standards of the era. “Well,

1

have

it,”

he

“We will simply send out two

says.

messengers,

each bearing an 8-digit binary number, and each bearing the magic

word “XOR” what

to

in the corner.

That

do when the messages

will tell

my colleague

arrive at the king’s castle.

“The number we want to send will be encoded in the final

the

same

message

is

to

be

0,

Merlin exactly

as follows: If a digit

then the two submessages will each have

digit in that place. If the digit

to be

is

1,

then the two sub-

messages will have different digits in that place.

“Here

how we

is

the final message

submessages, but or a

0.

We

will

might borrow

You writes a

1

in

0,

so

we must

a free choice

write the

second; lands

it

same

whether that

first digit

digit in

digit shall 1, tails

of

both

be a

for 0. If

1 I

”

a gold coin; he tosses

it

and

it

lands heads, so he

both submessages. digit

of the final message

is

to

of each submessage should be different.

again. If

it

be

we have

a coin

“The second digits

to

submessages. The

choose by tossing a coin, heads for

him

give

is

will generate the

falls

if tails, tails.

heads we will insert 0 in the

He

first

1

in the first

message and

continues in the same

have been generated.

1

be a

We

1,

first

will use the coin

message and 0

in the second.”

way

so the

in the

He tosses

until the strings

it;

below

220 / Schrodingers Rabbits

1

10101001

XOR

Submessage 2

11011101

=

Message

01110100

Submessage

Final

X

" '

“Now

its

The

is

coin.

string

own, each

and

its

own, each

also completely

it is

together yield the

down

different.

And true.

0

if

set

depending on the

digit also

number we want

yet

On

own

two

receipt of the

compare the successive

digits, writ1

if

they are

Sire.”

off he goes, clutching the coin. its

toss of

both messages taken

they are the same in both messages, but

Each number taken on

toss of a

depended on the

to convey.

Why, thank you very much.

first

random. And considering the

random. And

pieces of paper. Merlin has only to

ing

was

digit

considering the

Sire, that

is,

therefore completely

second submessage on a coin,

-

.

the marvellous thing

submessage on

^

is

What he

has said

random. Yet

is

perfectly

their relationship

contains a message.'^

To

fully

understand the ways a quantum system can contain

in-

we need to take one further step. The nonlocal correlations we have seen so far each required some information to be held locally, formation,

as pixel patterns in the first case

and binary numbers

in the second.

Even though the information in one submessage, or one page of pixels,

was not useful

to us

sense of the word.

on

its

own,

it

was

still

information in the

strict

The remarkable thing about quantum systems

is

that they are also capable of containing only nonlocal information.

Fortunately, even this can be illustrated with a classical analogy.

Let us

embark on another exotic adventure. This time we will sup-

pose that you are a secret-service agent in a foreign country trying to

communicate with a colleague who has been imprisoned fortunately the guards will not allow ject or

him

to

is

Un-

be given any kind of ob-

message, with one exception. Under local custom,

of the prisoner

locally.

some

friend

permitted (and indeed required) to pay for his meals

by giving the guards two coins, a nickel and a dime, each day. For

local

cultural reasons, the guards toss the coins in sight of the prisoner, al-

lowing him to see whether they land heads or spent.

tails,

before they are

)

New Age

The

Warrior: Anton Zeilinger / 221

This suggests a cunning plan to you.

A normal coin does

any information that can be revealed by tossing heads are just as

likely to

come up

as tails.

not store

in the sense that

it,

However, you discover that

by cleverly tampering with the coins you send, you can make them

nonrandom; you can make each one always you

as

your friend knows

please. If

message with heads coding for

one

day,

bit

and

1

fall

heads, or Ulways

you can send him

this,

tails for

tails,

a binary

0 at a rate of two bits per

per predictable coin. With patience, a message of any

length can be sent.

Unfortunately, disaster strikes.

The guards turn out

to

be not so

stupid as they appear. Before taking the coins to the prisoner, they

one a few times out of his

toss each

same way up every time, they untampered one. Your scheme Fortunately,

coins

The

more

result

heads or

treat

is

it

start rigging the

perhaps by inserting

tiny, cleverly

placed magnets.

is

equally likely to land

the two coins tossed together will always land either the

head, and one

whether

and substitute an

You

a better one.

same way up (both heads, or both

its

as suspect

that while each coin individually

tails,

coin on

it

keeps landing the

foiled!

you come up with

subtly,

is

sight. If any coin

first

tail)

own

depending on

tails)

or opposite ways up (one

how you

place the magnets. Each is

no predicting

toss.

However, both

contains no information; there

will land

heads or

tails

on any given

coins tossed and viewed together can code one bit of information, say,

0

(if

An if

they

come up

the

equivalent coding

same way) or

is

to say that

the logical proposition

true,

and

1

if it is false.

I

(if

they

come up

as opposites).

your friend should write down a 0

“The coins have landed the same way up”

Now

the guards

(who

are not

all

is

that bright)

accept your coins as random, and you will be glad to hear that your friend eventually escapes with the aid of the information that

him

at

one

The

dom, yet

bit

per day.

idea of a system

whose

parts appear individually quite ran-

exhibit curious correlations

when

taken together

reminding you of something, namely the photons experiment.

you send

Of course

is

no doubt

in the Bell-Aspect

the coin correlations are not really spooky, be-

cause they occur between objects that are not widely separated, but interacting via well-understood forces. However,

it

might be instruc-

/ Schrodingers Rabbits

222

N

tive to

remember that there was

distance effect of a

when the apparent action-at-a-

a time

magnet appeared

just as

EPR correlations seem

philosophers as

X

'•

'

spooky to contemporary

to us today.

-

Zeilinger’s Informational Principle

Now

we are in a position to understand the full flavor of Zeilinger’s new hypothesis. Conventionally, the information-carrying properties of quantum systems are derived from fiercely complicated at last

equations. Zeilinger’s approach

amount of information finite

and bounded. In

to

is

assume

as

the universe holds about a

an experimenter

his view,

an axiom that the

quantum system

who tries to measure

incompatible information about a quantum system

same kind of mistake

read 16 digits from an 8-digit register.

not there

—anywhere. His

The

ticles

know

that

we

if

requires

is

properties, the two-slit experi-

succession of photons or other par-

slits,

interference will normally produce a

The pattern develops

many

extra information simply

fire a

through two adjacent

pattern.

tries to

insight can be applied straightaway to the

most basic demonstration of quantum ment. .We

making the

is

computer programmer who

as a rookie

is

bits to define

slowly; a clear interference-band picture it.

If

you watch the pattern

build,

it is

much like downloading a picture from the Internet through a slow modem. TEie first few hundred bits give only a blurry view, which becomes gradually sharper

more

as

bits are transmitted, as

shown

in

Figure 15-4.

But

if

any attempt

is

particle passes through,

made

to

however

ployed, the interference pattern Zeilinger’s view, this

is

trajectory information.

measure which of the two delicate or indirect the is

slits

means em-

destroyed, as in Figure 15-5. In

because each particle carries just one

We can

each

bit

of

use this bit either to get which-slit in-

formation or to increase the definition of the picture on the photographic film, but not both. particle,

because

right) to specify

it

you measure

takes exactly

which

ture information,

If

slit,

we measure one

tfiere is

and your film

will

the trajectory of every

bit (coding, say,

no capacity

0 for

left

and

1

for

left

over to code pic-

show a random

pattern of dots. If

only, say, half of the photons, the pattern that builds

up

The New Age Warrior: Anton Zeilinger / 223

FIGURE

15-4 Two-slit interfer

ence pattern.

224 / Schrodingers Rabbits s.

FIGURE

will

No

15-5

pattern.

be blurred as in Figure 15-6, because only the nonmeasured pho-

tons can contribute picture information. Each bit can be used only once; trying to obtain both trajectory information and interferencepicture information to use the

same

picture data

from a limited number of bits

area of

computer memory

—something

Zeilinger’s

for

—

it

can

trying

inevitably gets corrupted.

view seems to imply that

know the

much like

both numerical and

much

(or perhaps even

the information the universe-computer contains ture

is

relative status

is

all)

of

relational in na-

of two variables, without storing

any information about their absolute values. In terms of our parable of the besieged

castle, the

message to Merlin

computer knows the contents of the

— but

it

overall

holds no data about the individual

submessages carried by the two runners. This leads Zeilinger to the idea that the fundamental information in the universe-computer

should be regarded as logical true-false values of statements about

quantum

systems.

Zeilinger has proved that properties of

quantum systems

that are

The New Age Warrior: Anton Zeilinger / 225

FIGURE

15-6 Partial pattern.

often considered weird, like the correlations obtained in nonlocal

mea-

surements, follow logically from this principle. His starting point

is

a

simple system., the two photons of the Bell-Aspect experiment. Zeilinger finds that the universe-computer holds only

two

formation to describe their joint polarization, measured angles.

These two

bits

bits

at

of in-

whatever

can be considered as the truth values of the two

statements,

“The polarization of the two photons, measured tions, will be the same.” (Always TRUE.)

in parallel direc-

“The polarization of the two photons, measured will

at right angles,

be the same.” (Always FALSE.) For this system,

information. There

all is

that the universe-computer contains

no information capacity

left

is

relative

to store the states

of the individual photons. Zeilinger finds that from these assumptions,

he can recreate the spooky correlations of the

on

to derive a

field,

more general

result,

Bell inequality.

He

goes

which, exceptionally for this arcane

can be rewritten in simple English: “Spooky correlations can arise

226

/ Schrodingers Rabbits %

in a

simple quantum system

formation

is

when more than

used to define joint properties

half of the available in-

”

Thus the two-photon system of the Aspect experiments turns out to be, surprisingly,

adcrit

moi^e

quantumy than

the

minimum necessary

for Bell correlation effects to occur. %

An Informational

Interpretation?

new way

Zeilinger has certainly found an interesting

to look at en-

tanglement. His success in explaining nonlocal behavior from straight-

forward assumptions

is

solid Occam’s-razor justification for his

hypothesis that, at the most basic

level,

the universe might contain

information about individual quantum systems rather than individual

He presumably hopes

localities.

that his approach can be extended

mathematically to determine the behavior of more complex entangled systems. If this were to throw light

on the way

that relative informa-

tion in small systems tends to “turn absolute” in larger ones,

new way to look at quantum

provide a

it

could

collapse. Unfortunately, previ-

*

ous attempts to extend such “measures of quantumness” to large

sys-

tems have run into a morass.^ Zeilinger’s

view also shares a problem with

much

less

worthy

at-

tempts to brush aside the problems of quantum, namely the questions: If the universe

is

intrinsically nonlocal,

why

is

the illusion of

Why do causative effects always propagate at less than the speed of light? Why are forcelike interactions stronger at short

locality so strong?

ranges? Nevertheless, real physics

if it

turns out to be possible to generate further

from an extension of his axioms,

taken very seriously. Perhaps stuff,

and the

it

out that quantum

will turn

illusion of locality arises as

of the algorithm the universe-computer

way

to

have to be is

the real

an almost incidental feature

is

running.

do not believe that

Zeilinger’s

approach

will

understand the quantum world.

When we

dis-

Personally, however,

lead to the best

his ideas will

I

cussed the merits of different interpretations in the context of ticktack-toe,

we decided

that

intuitively able to play. In

method

is

it

vital to find a

game

that

humans

are

terms of the tick-tack-toe analogy, Zeilinger’s

like trying to play the

adds-to-15 game.

Our human minds

The New Age Warrior: Anton Zeilinger / 227

are designed to perceive the world in A visuospatial

than in terms of abstract Zeilinger’s

logic.

However mathematically

approach turns out to be (and

overcome), we would

still

way more

it still

easily

successful

has major obstacles to

need the equivalent of a magic square to

translate his informational universe into

one we can readily visualize.

V S*.

CHAPTER

16

\

"

PROVING AND IMPROVING MANY-WORLDS

A

we have established that the many- worlds view is a valuable thinking tool, worthy of its place among interpretations of quantum. Certainly it is the best way to think t

the very least,

about the interaction-free measurements described in Chapter

With the modest sist until

world,”

a

principle, “Interference effects

measurement of the

we were

10.

between worlds per-

self-interfering object

is

made in either

able to understand the workings not only of the

Elitzur-Vaidman and Zeilinger designs, which use photons following different trajectories tly

from the one

in

our “own” world, but more sub-

the Paul-Pavicic monolith experiment that uses a photon that

at a different I

time than the one in our

own

left

world.

suspect that even considered just as a conceptual model,

many-

worlds has a great deal of further mileage waiting to be wrung out of it.

For example, no one has yet given a

particles

simple picture of

can “quantum tunnel” forward faster than

information faster than etically speaking)

in

clear,

light.

The

idea that

we might

have swapped the particle that

“our” world for one that

decohered other world

is

left

at least

just

an instant

an interesting

22S

light, yet

left

not carry

(loosely a

why

and po-

moment

later

earlier in a not-yet-

try;

the principle above

Proving and Improving Many-Worlds / 229

illustrates

why

tinkering with either pfarticle

would have broken the

connection, ensuring no message could hop ahead faster than

light.

when we make a measurement on an entangled system we are in some sense “dialing in” to a world in which other parts of the system are likely to have certain values relative -to^our own explains how we can later find we have obtained spooky correlations The

idea that

with far-flung parts of the system, without any question of being able to cause effects on those parts. (The dialing-in metaphor must be qualified

by a

one phone

restriction like the rule that arrested persons

call

only before being isolated in a

weak spooky link once you have used It

seems quite

likely that

cell.

You

can make

lose even this

it.)

mix- n-

extending this “dialing in or

match” rule of thumb might help visualize other features of entanglement, for example, giving us better insights into such phenomena as so-called quantum teleportation. If a richer view of many- worlds gives us better insights into ers,

how to

design such things as

the imaginative effort will have been well worth

Other worlds are

at

any rate a useful

of demonstrating that many-worlds tion, or to

put

it

is

illusion.

But

more than

it.

is

just

there any

hope

an interpreta-

another way, that those interpretations that do not

accord other worlds equal status to our

cal

quantum comput-

own

are falsifiable?

David Deutsch and Lev Vaidman have each proposed hypothetiexperiments that would “prove” many-worlds by demonstrating

we would normally think of as havdecohered from our own. For example, if we could

interference with world lines that

ing irreversibly replace the

photon or electron normally

fired

through a two-slit ex-

periment with a capsule containing a conscious observer, the observer might show signs of having been “affected by” both worlds when she

emerged from the experiment. She might, for example, say that she clearly remembers that she could see which of the two paths she was

—but somehow cannot now remember which

going along

it

actually

was.

These experiments would require incredibly advanced and elaborate technology, however. This has

two disadvantages. The

first is

that

no such technology is available, nor will it be for the foreseeable fuImagine ture. The second is what 1 call the “Jurassic Park” argument.

«

230 / Schrodingers Rabbits

two

that

exist;

scientists are

they

make

arguing furiously about whether dinosaurs

on the matter. One guy goes

a large bet

mining Antarctica

one by heroic

to reconstruct

same fashion

and by

for deep-frozen dinosaur DNA'J' etc., he eventually

produces a dinosaun-I/id he prove that dinosaurs

was possible

off

still

feats

exist or just that

it

of data retrieval? In the

might say that.Deutschs and

a skeptical single- worlder

Vaidman s experiments prove nothing more than

that

you can

create a

kind of artificial dual-world simulation by creating circumstances that

would never

arise naturally.

David Deutsch has claimed that the

can the resources for

all

that computation be

unfortunately, any proof that a tally is

outperform a

obtained,

of

quantum com-

much “proves” the reality of many- worlds because where

puters pretty else

feasibility

it

classical

tain extra degrees of

decoherence can occur decohered world

show only

freedom

far,

quantum computer can fundamen-

one remains

will, arguably,

coming from? So

—

— rather

lines effectively

that

elusive.

And even if that proof

that our world possesses cer-

what Gell-Mann

weak

calls

than the existence of strongly

independent of our own. There

is

«

always an understandable temptation for proponents of any particular

quantum

interpretation to see stronger evidence for

it

than a par-

ticular

experiment provides. For example, shortly before

went to

press,

book

this

an ingenious experiment by Shahriar Afshar was claimed

to have “disproved”

both the Copenhagen and the many- worlds

pretations.^ In fact,

it is

inter-

modern manyinterference effects from

exactly consistent with the

worlds view, specifically the idea that

“other-worldly” photons continue up to the point where a measure-

ment

is

made. Afshar’s experiment demonstrates wavelike behavior

followed by particle-like detection, just like our

bomb

detectors.

how satisfying it would be if we could directly prove the existof other worlds! Max Tegmark has one idea for a relatively low-

But ence

tech experiment to

do

Russian roulette idea

so. It is

simply an iterated form of the quantum

we have ajready met. The idea is that you rig up

kind of machine gun that

fires

a

one shot per second. However, each

second a quantum randomizihg device, the equivalent of a coin

toss.

Proving and Improving Many-Worlds / 231

determines whether the gun will use a photon that

is

the photon

ror. If

Hve shot or a blank. You could

fire a

reflected or transmitted

gun

transmitted, the

is

by

a partly silvered mir-

fires a

blank

bullet; if re-

flected, a live one.

Having

set

up the

device,

dent that the usual laws of

you

give

it

statistics will

a test run. Youri^n be confi-

be obeyed

set up.

click, click,

But

You

will

hear a sequence something

after

100 shots,

dummy target

there will be approximately 50 bullet holes in the

have

—

like:

you

Click-BANG!,

click-BANG!, click-BANG! ....

now you step

in front of the device yourself: Click, click, click,

click, click, click, click.

.

.

.

Now you

observe a blank every time. Each

time the gun operates, you are halving your measure of existence. But just of course, you are not aware of those worlds in which you have ceased to

exist.

To you,

it

seems you are

know your chance of survival 1,000. After 20 clicks,

time,

you can prove

1

world

in a classical

in a million. After 30,

to yourself the device

Immediately the laws of chance

aside.

invincible. After 10 clicks,

is

is 1

than

in a billion.

in a

1

At any

working just by stepping

(as seen

view) return to normal. The intermittent

just less

you

live

from your point of

shots start

up

again.

Tegmark points out a snag with the device (that is, a snag over and above the reservations about quantum suicide listed in previous chapters).

He argues that you can convince only one person by the method,

namely

yourself.

Suppose your colleague Professor Cope heroically

volunteers to take the stand. You can be virtually certain that after a few shots you will be looking down in horror at the body of the fa-

mous

physicist.

However, here Tegmark has perhaps not considered quite the whole story. To see why, suppose you invite your secretary in to witness the procedure. ^*Don’t worry, figured out a clever reason

And you

Now

you

why you

tell

her mendaciously,

will see

me

I

have

survive every time.

start the device.

in

most of the resultant worlds, your secretary

will very

her opinshortly be shaking her head in sadness but not in surprise as ion of her boss’s sanity

is

finally

confirmed. But those worlds do not

witmatter to you. In the worlds that do matter, she (and any other science) are nesses yc>u might have invited, such as philosophers of

232

/ Schrodingers Rabbits

gazing at you with an increasingly wild surmise. Those

know that

physics

the laws of

quantum do not

And

sequence of luck they are seeing. eyes. If you are unscruf)uloq,s

to divine intervention,

end up

soon quite a

it is

explain the miraculous

ha^)pening before their

to claim that your survival

is

due

of the people in the world you

lot

As you continue'

in will believe you.

spite the

enough

yet

who know their

to survive every time, de-

most rigorous checking of your equipment by independent

experts, even the

most hardened

skeptics will begin to

wonder

In fact an analogous procedure was suggested in a detective story

written decades ago.

The

basic idea

was

to

send

letters to a large

batch

of randomly selected people claiming that you have inside information

and can predict the

of the

letters

After Sunday,

wrong

result of

you send predict

Sunday s big game. But

side

A

will

win, the other half side B.

you discard whichever half of your address

tips to,

actually half

list

you sent

but write to the other half a second time with a

new

prediction for next week’s match. Again you split your prediction, and are

left

with a quarter of the original batch that

is

you. After a month, the small batch remaining

know what you

are talking about,

from your knowledge by placing

is

beginning to believe convinced that you

and most of them have profited

Now

bets.

infallible tipster service will continue,

you

tell

them

that your

but the annual subscription

is

$10,000 payable in advance In the Qriginal story, the protagonist unintentionally creates a dan-

gerously fanatical cult of people

who

believe in

him more

strongly

than he ever intended. That story was written before the days of the Internet, but in the present e-mail era the feasible.

(Come

to think of

it,

some of the

could quite possibly be generated on suicide version, however,

scam would be

financial-advice

this principle.) In the

you end up not with

perfectly

spam

I

get

quantum-

a handful of people to

whom you appear infallible, but a whole world. 'QjyQjyQn It

would obviously be

desirable to have a less dubious

method of

proving many- wo rids. In the mid-1990s, Rainer Plaga of the Planck Institute proposed a first

less

dangerous experiment.^ The idea

Max is

to

create a miniature Schrodinger’s cat, an ion in a state of quantum

Proving and Improving Many-Worlds / 233

measurement

superposition, and then do a separate

by

clearly signaled world-split, for example,

firing a

that causes a

photon into an

apparatus that lights either a green lamp or a red one, depending on whether a photon is reflected by a half-silvered mirror. Plaga s reasoning

is

essentially that because the ion in

know whether

the green or the red

contact with both worlds.

—by

Thus

a

its

lamp

magnetic cagordoes not yet lit, it

remains in effective

measurement interaction triggered

—

beam at the ion, for example could cause an effect in the other as the quantum superposition is destroyed. For example, it could cause an electron to be emitted at that moment. in

one world

If

firing a laser

the experiment works,

from one world to the other

it

can be used to convey information

in a one-shot kind of way.

Here

is

how it

could be used to convince a many- worlds skeptic. Ask him to invent a six-digit

number unknown

which he holds the only

to

anybody

and lock

else

it

key. Explain that the rules of the

in a safe to

experiment

on the green-orhe must open the safe and

are that just before midday, a button will be pressed

red-lamp device. tell

If

the green light shines,

you the number. But

locked

—and

if

the red light shines, he can keep the safe

midday, you will

just after

tell

him

the number, trans-

mitted as a signal from the other world where the green lamp shone.

The experiment

is

run; the red light shines.

ment, a few m.oments

though

it is still

later

you can

locked in the

To the

him

tell

skeptic’s astonish-

his secret

number, even

safe.

how the trick is done. If the green light shines and the safe causes the is opened, you read the number and set a timer that Schrodinger’s-cat ion to be interrogated by a laser beam at exactly the Here

is

midday corresponding to the value of the six-digit integer. In the parallel world where the red light shone, the ion emits an electron as its twin is interrogated. By measuring the

number of microseconds

after

exact time at which the emission takes places in microseconds past

midday, the code number

do the experiment, you

is

will

discovered.

end up

Of

in the

course half the time you

world where the green

light

and become the transmitter rather than the receiver of the information. But all you have to do is keep repeating the experiment. In

shines,

half of the runs, that

is

on average, you

known only to

get to

show

the skeptic information

himself and persons in the other world.

/ Schrodingers Rabbits

234

N

This would be a repeatable and utterly convincing demonstration of many-worlds. Unfortunately, very few physicists think the experi-

—Plaga himself put

ment would work

overwhelmingly majority yiew decohere

at the

moment

it

forward bnly

that the worlds

is

and red lamps

the green

gent versions of the Schrodinger’s-cat ion.

To

tentatively.

The

would completely

lit,

including diver-

the best of

my knowl-

edge, the experiment has not even been tried in the decade since

it

was

proposed.

Last night I

I

had a dream

was sharing

a lab office with Professor Cope, the impressive old

gentleman we met

in

Chapter

1.

you may remember. Cope had the

many- worlds

his

new scheme

theory, but

This was proving to be quite a at first

as

now he was insisting on telling me about

for transmitting messages

he told

me

As

been most reluctant to accept

between worlds that had

completely decohered and gone their separate ways.

him out

trial.

the details

(I

now

I

managed to tune

regret to say), but ignoring

the banging as he constructed an odd-looking device to be connected to his

computer was more

expectant

difficult.

Presently he turned to

an

air.

“Congratulate me!” he announced.

“I

have connected the camera

on top of rny workstation so

that

copy of my computer screen

in a parallel world,

I

me with

speak into

it

will transmit a picture to

and

another

vice versa.

Words

my microphone will also emerge in the headphones of my

other self in that adjacent world!”

He

pointed

at his

workstation, which was displaying a picture of

He waved, and the image mirrored the action. “But now watch!” he said, throwing a bulky switch. “That

himself.

simple

communication between two diverging worlds, in photon was reflected, in the other transmitted.” He

action established

one of which a

waved

him

his

arms about. The picture on the screen continued to copy

exactly.

He looked

mildly disconcerted.

“Harry,” he said loudly, presumably trying to speak to the other

version of himself, “yow raise your hands above your head, I will hold

mine out

to the sides.”

He held his arms

out to the sides and the image

Proving and Improving Many-Worlds / 235

on the screen duplicated

his action e^^actly.

experiment was a

He was

fiasco.

was obvious that

It

own

merely continuing to see his

picture in one world. Eventually he went

home

in a

bad temper,

his

leav-

ing the computer turned on.

The following day

I

arrived at the lab to be greeted

voice from Professor Cope’s computer. “Well, it

I

a sarcastic

you

see that

re on time,”

said. I

looked

seemed

at the screen. It

to be

showing Professor Cope

was empty. The image grinned.

sitting in his lab chair,

but the

“That’s right,”

“I’m the Cope in the world next door to you.”

it

said.

“Very funny,” at

home,

getting

I

replied. “I

real chair

suppose you’re

sitting at

some fancy graphics software

background of the lab

here. Well,

it’s

your computer

to display

not April

First,

you with a

and

m

I

not

fooled.”

The image shook

its

head.

of your Professor Cope. In

“No

fooling,”

my world

it

said.

“I’m a

little

ahead

an insect blew into the window

morning, and the bang woke me. Your version seems to have

early this slept in.”

At that

walked

moment

the lab door opened and Professor

“Beat you!” called the image in the screen.

in.

and appeared genuinely flabbergasted. “I got into work a couple of hours hour ago, so about

to think

all

this

Cope himself

Cope looked

I’ve

at

it

had more time

than you,” the image said to the physical Cope

“Of course when our worlds started to diverge yesterday, they were incredibly similar, with only one photon’s worth of difference between them. No matter what the two of us did, we couldn’t help cheerfully.

acting exactly like the

same person. But as time passed, butterfly effects

magnified the difference so that we started to act really are

“Pull is

two of us, with completely

up

incredible

And worlds

is

a chair

and

I

to

be

woke

Now there

thought patterns.

listen to the plans I’ve figured out.

—we’re going

then, of course,

different

differently.

This thing

rich!'

up.

Communication between

fun to explore as a science-fiction theme. In

parallel

my opinion

the

consequences that would follow have not yet been worked out as thor-

oughly narios

in

contemporary science

— time

travel,

fiction as other hypothetical sce-

matter transmitters, and so forth

—were explored

236 / Schrodingers Rabbits

back in the golden age of

sci-fi.

temptation. But on almost

all

you can

interact with

It is

Perhaps one day

will yield to the

I

present indications, parallel worlds that

remain the stuff of pure

fantasy.

too soon tO"be absolutely dogmatic about

this.

We

do not

yet

understand everything about decoherence, or about the relationship

between quantum and general

relativity, to

name just two

areas.

It

has

even been suggested that many- worlds could solve a troubling paradox

—

modern physics that general relativity implies that at least one method of time travel is possible. In a single world line, obvious conof

tradictions could arise

if

you

many-worlds perspective, ing (depending lines,

all

try to

change your

own

you would be doing

on which way you look

at

it)

is

past.

But from a

creating or enter-

new measures of world

diverging from those that produced your original memories.

A more promising line of approach, however, is to

strengthen the

philosophical case for many-worlds. Let us start by further disparaging the idea that the supposed extravagance of the many-worlds view is

a reason for rejecting

it.

Deutsch in particular has pointed out that the many-worlds pretation

wave idea

—

inter-

Bohmian mechanics the particle-plus-guidewe followed at the start of the book minus the idea that

is

very

like

—

there are particles riding the waves in just a few particular positions.

As he points out,

if

we

accept the reality of the waves,

why ever should

we assume that all but a few positions on the “sea” are empty? Lev Vaidman has put it more poetically:^ “If a component of the quantum state of the universe, which is a wave function in a shape of a man, continues to move (to live?!) exactly as a man does, in what sense it is not a man? How do I know that I

am

not this ‘empty’ wave?”

Of

course,

Bohmian mechanics

is

not the only alternative to

many-worlds. But again, as Deutsch has pointed out, other approaches

some kind of local-fixed-reality are actually even more If we forget the .worries about backward-in-time para-

that allow for

extravagant. doxes,

and assume

that

Bell-Aspect experiment

when, it

for example,

really

we

test

one photon

in a

does communicate with the other via

.

Proving and Improving Many-Worlds / 237

imagine

a faster- than-light signal, just to

and

with

on.

Every time a particle decides what to do,

the other particles that

all

fore to sult

fro.

all

it

must consult

has ever interacted with (and there-

it

some degree become entangled

with

how many such signals must go

with),

which

in turn

must con-

the particles that they have ever interacted^with, and so

We must

postulate an absurd

amount of behind-the-scenes mes-

saging going on, which at least rivals the supposed extravagance of the multiverse.

But

now

let

more

us take a

aggressive approach. Let us

demon-

two possible ways to wield Occam’s razor very strongly in support of the many-worlds view. The first is based on an insight of Max

strate

Tegmark’s; the second

is

my own.

Although we only have one universe to examine, certain of its tures are very striking. In particular, the physical laws defining

havior are remarkably few and algorithmically simple written

on

be-

—they can be

a single sheet of paper. Its starting condition, essentially as

a single point,

tation

its

fea-

was

also simple. This

—although perhaps

it

conforms

to

our

intuitive expec-

generates our intuitive expectation

—

that

by a small amount of information, however large the volume of space and time it might eventually expand

a universe that can be defined

into,

is

much more likely than a universe embodying a vast set of rules

or a quirky set of

initial

information to describe

Max Tegmark

conditions that would require a great deal of it

has identified a troubling problem with this cosy

The universe that mind-boggling amount of detail. The

“universe from a tiny package of information” view.'^

we

see

around us contains

a

general pattern of the universe that

understand, by the

phenomenon

ery region of the universe are sufficiently similar

—

we

see can be explained,

we now

called self-organized complexity. Ev-

—and indeed of any universe whose

will contain stars, galaxies,

rules

complex organic

chemicals that give evolution a potential starting point, and so on. But

we

also see a great deal of specific detail that

such general

rules.

cannot be explained by

Why is the play Hamlet worded exactly as

it is,

for

example, and written in an alphabet using 26 characters? Although the text of that play, like almost any long text written in the English

language, can be compressed by a factor of several using clever

com-

— 238 / Schrodingers Rabbits

puter algorithms, the irreducible

amount of information

in effect, the length of the shortest

—

produce the play exactly

To describe the let

is still

computer program that could

of the order of 1 010,000 binary

even^the planet Earth and

state

contains

it

its

re-

digits.

contents exactly,

alone that of the whole visible universe, would take an enormous,

perhaps

infinite,

amount of information. Where did

all

that informa-

come from?

tion

Tegmark has

we

a simple answer. If

every physically possible

live in a

multiverse in which

quantum outcome occurs, the detail is merely

a kind of observer illusion. There are equally valid universes in

which

many slightly different forms. And who wonder why it took exactly that form. It

the play Hamlet, for example, takes

each contains observers

takes less information to specify a multitude of possibilities than

does to specify a single

possibility.

of the result of tossing a

To write down a

classical or

requires a million binary digits. But to

quantum tell

you

specific

it

sequence

coin a million times

that the result

is

equal measures of universes in which each of these sequences occurs takes just a single sentence. *

Although Tegmark does not use the metaphor, there thetical library that philosophers are

his idea very well.

It is

is

a hypo-

fond of invoking, which sums up

a library containing every possible

book

that

could ever be written, and yet no useful information! Figure 16-1

shows a simple computer program, storable nary

digits, that

in fewer than 1,000 bi-

can generate the exact text of Hamlet. In

fact

it

can

generate alternative versions of Hamlet that are better than Shakespeare’s,

and indeed the

text of every other

written or can ever be written that glish letters

a million

and the

common

is

that

was ever

composed only of standard En-

punctuation marks and

less

than about

words long.

The program shown

really

could

—

at least,

computer and a very large supply of paper

program

will

given a very durable

—generate the hypothetical

library the philosophers are fond of describing.

the

book

The

first

iteration of

simply print out in sequence every possible book

we allow upperand punctuation marks. The second itera-

only one character long^about 100 of them

that

is

case

and lowercase

letters

if

)

Proving and Improving Many-Worlds / 239

START

FOR BookLength = 1 TO 7000000 CALL GenText(BookLength, NEXT BookLength STOP SUB

GenText(Lremaining, S$ IF Lremaining = 0 THEN End Of Book PRINT S$ + “

”

ELSE

FOR I = 20 TO 120 CALL GenText(Lremaining

-

1,

S$ + CHR$(I))

NEXT END IF END SUB FIGURE

16-1

I

A program cleverer than

tion will print out

Shakespeare?

around 10,000 books containing every possible pair

of characters, and so on. The library produced will be exhaustive, but it

will

not be very useful. But

If a particular

Hamlet could

it

does make Tegmark s point rather well.

arise

just the

way

it

happen

to

the sequence of events

me?” the unsympathetic answer

is,

“That’s

looks to you. Actually, every typographically describ-

able sequence of events

where

text of a particular version

“Why should

of the play in the library and ask just described

from the

happens to some equally

real

Hamlet some-

in the library!”

The multiverse generates every physically possible sequence of and requires very little information to set it events simultaneously

—

going, just as the book-writing is

more

plausible that

we

are just

in a universe that requires

we

program above

little

one of many

is

very short. Surely

sets

it

of creatures living

information to describe

it,

than that

are a unique set of creatures living in a universe that requires a lot

of information to describe

it?

240 / Schrodingers Rabbits %

Constructing a Local Universe %

One

great advantage of a multiverse as a visualization tool should be

its locality,

the avoidanfce of the need to postulate instant long-range

we mentioned David Deutsch’s key paper which proves this, and we described some metaphors like “dialing in” to a particular world when you measure an entajigled system. influences. In an earlier chapter

we have not really gotten the full benefit of multiverse locality in a way we can feel in our bones. As the philosopher Jim Cushing put it, we need to tell ourselves local stories in order to feel that the universe is working in a commonsense way. We need a story in which But so

space

far

is

filled

with entities that have effects only on their immediate

neighbors, and in a well-defined temporal sequence.

The universe

I

am asking you to visualize is, of course, a hidden-local-variable theory. And I would suggest, very controversially, that that such a thing set

is

possible

—

that

it is

tells

us

board on which

to

Deutsch’s result

a legitimate

out to play tick-tack-toe with the gods, a potentially valid way to

look

A

at things.

hidden-local-variable multiverse theory can

where a hidden-local-variable this

is

possible in principle.

single

world

line cannot.

Have we any way

to put

work

We know that

some

flesh

on

the

bones, to deduce the properties of the postulated unobservable cog-

wheels whose turning supports the persistent patterns we can see?

The

first clue,

of course, comes from the fact that the hidden vari-

ables are indeed hidden, not directly observable

much more

us.

—

in

know

that

if

you

are

anywhere

—be

which the laws of physics operate

way, with things bouncing about

elastically,

it

in a

variables.

On

the contrary,

pattern or “permanent” record

We

is

there

is

no reason

can actually find

space supports

classical

we used

computer made of optical

the goingspersistent

special process.

processes that hardly interact.

featured a fibers

and

to ex-

systems in which a single region of

many independent

earlier illustration

all

making any kind of

a rather rare

is

a universe or a

time-symmetric

pect that any observer should be able to see and record

on of the

This feature

disconcerting to the layperson than to the physicist, be-

cause physicists multiverse

by

man-made

An

object of this kind, a

through which different wavelengths

of light are transmitted by deliberately contrived arrangements of

fil-

Proving and Improving Many-Worlds / 241

More convincing would be an example of

ters.

space that

is

Allow

a

volume of empty

shared by largely separate processes.

me

living in interstellar space

They

you

to the Radioheads.

who

are so tiny, or so ghostlike, that they

to introduce

are creatures

never affect one another by direct physical contact. They perceive one

another because each has a precise frequency,

and

little

built-in radio transmitter set to a very

population of Radioheads can

initial

same frequency. Thus the

a receiver set to the

perceive

all

and

talk to

one an-

other.

Alas,

mutation does

its

work. Each baby Radiohead

is

born with

receiver-transmitter set to a very slightly different frequency

of

its

parents.

spring,

and

Although

vice versa,

all

some of

the offspring can perceive each other it

comes about quite naturally

any one Radiohead perceives only a tiny subset of the

lation.

As

far as

he

is

on his existence a

of background noise. The descendants have that will never again reunite. I

total

popu-

concerned, most of his distant cousins have passed

into invisible ghosthood, their only impact

Admittedly

from that

the parents can see and talk to their off-

only dimly. As the generations pass, that

a

faint hiss

split into different species

They have decohered.

invented the Radioheads. But there

is

at least

one

natural cosmological process in which different entities can share the

same volume of space with That

is

the situation where two galaxies or clusters of stars collide at

high speed. Actually “collide” place, because stars are

is

a complete

stellar

physical collision between pairs of stars axies pass

for

what

takes

neighbors that the chance of is

virtually negligible.

The

gal-

through one another and continue on their separate ways.

The only

interaction

is

gravitational.

rather significant. In our galaxy, our its

misnomer

such tiny things in proportion to the vast gulf

of space that typically separates

from

between them.

relatively little interaction

Sun

You might expect is

more than

that to be

four light-years

nearest reasonably massive neighbor. Alpha Prcximi. If an-

other similar galaxy were to pass through ours at high relative speed, a

number of its stars would be

statistically likely to pass the

fraction of that distance. However, the direction

Sun

at just a

and magnitude of the

tiny gravitational force that Alpha Proximi exerts remains roughly con-

stant over thousands of years, adding

up

to a significant effect.

By com-

242

/ Schrodingers Rabbits \

parison, the gravity from those stars of the other galaxy that passed

near the Sun would exert forces only briefly, and in essentially directions. Galaxies that pass

speeds have relatively

Allow

little

through one another

gravitational effect

high relative

on one another.^

me to promote you to godhood. You

are in charge of creat-

and one of time,

ing a universe with three dimensions of space like

at

random

just

our own. You can populate the universe with whatever kinds of

and other things you

fields

like, as

long as they interact only

locally.

For bonus points, the rules of your universe should permit interesting patterns to arise. I

put

it

to

you

that in general there

is

no reason

to expect that

your

rules should cause every pattern to continue to interact with every

other pattern. That

actually a rather special case. In biology, the laws

is

of evolution naturally cause species to

no longer

interbreed,

and diverge

reactions so specific that two or

be taking place in the same

on one another. In

physics,

way as

different chemical processes can

tube while having virtually no effect

two water waves can pass through one

another and each continue on a

subspecies that can

thereafter. In chemistry, there are

more

test

split into

way almost unchanged.

its

these, patterns that interact only

In just such

with a small subset of all the

other patterns around should be considered the

norm

rather than the

exception.

Lattice

Models

What specific facts can we deduce about our hypothetical hidden variables? Here we must make a diversion into a different area of physics. It is

a still-emerging field, the arena of strings

theories.

digms

Not

just the fine details,

related

but even their most basic para-

—the number of dimensions and the very topologies—of the

entities involved are

still

being hotly disputed. But the basic aim was

summed up by Richard Feynman when It

and loops and

always bothers

me

that,

he wrote: we understand them number of operations to

according to the laws as

computing machine an infinite figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that

today,

it

takes a

tiny space? ....

I

have often

made

the hypothesis that ultimately physics

Proving and Improving Many-Worlds / 243

will

not require a mathematical statement, that in the end the machinery

will

be revealed, and the laws

board with

all its

will

turn out to be simple,

like the

checker-

apparent complexities.

^

Caricatured in the simplest terms, string theorists are looking for a

model of the universe

space divided into tion,

cells,

that will be like a cellular autofnaton, with

each of which contains one bit of informa-

and which evolves according to simple local

Conway’s famous game of

Life, as

shown

Life are very simple: place counters

on

rules a

little like

in Figure 16-2.

The

John

rules of

a checkerboard. Each turn, re-

move every counter that has fewer than two or more than bors, but place a new counter on any square that has

three neighexactly

two

neighbors. These rules turn out to be capable of supporting processes

of unlimited complexity. Figure 16-2 shows a simple Life position progressing through successive time steps.

Almost no one expects that the fundamental structure of our universe will turn out to be something quite so simple as a cubic lattice

with each cube containing one bit of information, as a naive extrapolation

from

would imply. The simplest plausible topology is someshown in Figure 16-3, where space is described by some

Life

thing like that

kind of continuously morphing network of locally connected to

conform with

special relativity’s prediction that there

is

vertices;

no

special

frame that can be considered stationary, the vertices would not be static,

but would vibrate about

There are these models infinite

many is

at the

speed of light.

other possibilities. But an essential feature of

that rather than every region of space containing an

amount of information

—

as

would be

required, for example,

to define the exact value of a classical field at every point

the region

only a

—

finite

a certain

a given

volume of space, say

number of binary digits

another way,

it

all

1

cubic centimeter, requires

to describe

its

would be fundamentally impossible

number of bits of information

throughout

state precisely.

to store

Put

more than

in a region of space of given

size.

how many bits? What is the notional volume required to store a single bit? Presumably it must be very small. An early guess was based But

on

a unit called the

foot

Planck length.

and the meter are arbitrary

Human

measures of length

like the

(the true origins of the English foot

244 / Schrodingers Rabbits

n n n n n nn

n

n n n n FIGURE

16-2 John Conway’s

n n n n

Game

n n

n of

Life.

n n

Proving and Improving

FIGURE

16-3

The

Many- Worlds / 245

idea that the fundamental particles of physics are merely topo-

logical features or knots in the fabric of space-time dates

back

at least to

the Victo-

rian notion of ether vortices. But the precise nature of the entities involved

we talking one-dimensional strings or two-dimensional membranes, and embedded in a space of how many dimensions? This picture is

continues to be argued. Are

almost certainly an oversimplification.

are lost in the mists of time; the French meter represents a slightly

inaccurate guess at ence, intended to

1

forty-millionth of Earth’s equatorial circumfer-

make

navigational calculations easier).

More funda-

mental units are those based on the constants of nature, the most familiar of which

is

the speed of light, usually written as

an alien in a radio message that

if you

told

him

the speed limit was one

light, that is a universally

tional constant, defining the

And

a third

which defines the

is

ratio

you told

1

how

fast that

was,

-millionth of the speed of

meaningful measure.

Another such fundamental value

induce.

If

in Britain, autos are restricted to a top

speed of 70 miles per hour, he would have no idea but

c.

in

our universe

is

the gravita-

warping of space that a given mass

Planck’s constant, which

we met

earlier

will

and

between the frequency of a photon of light and

amount of energy it carries. By appropriate multiplication and division we can derive the basic units of mass, length, and time from these values. The fundamental unit of length, the Planck length, turns

the

out to be 10"'^

tiny,

roughly 10"^^ meter (for comparison, a proton

is

about

meter in diameter).

There

is

a very

hand-waving argument that the fundamental

in-

V •

•

246 / Schrodingers Rabbits K

%

formation density of space should be on the order of

1

bit

per cubic

Planck unit. In 1973, this guess received a curious kind of confirmation. Jacob Bekenstein discovered,^ in

work

later refined

by Stephen

^ space "Containing a black hole, an event

Hawking, that the region

horizon, has a physical quantity called entropy associated with

which

in turn implies a quantity

experiments involving general

viewpoint of an observer

who

of information. By simple thought

relativity (for is

it,

in

normal

example, considering the

space, but accelerating),

it

can be demonstrated that not just a black hole, but any region of space,

amount of information. But there was a The amount of information any region of space,

can contain only a shocking surprise.

finite

however shaped, can contain its

is

proportional not to

its

volume but

to

surface area!

This result has been dubbed the holographic principle. The Nobel

winner van

Prize If

’t

Hooft has given a memorable way to visualize

you imagine the surface enclosing

computer

screen, each of whose pixels

this.

a region of space as a flexible is

2x2 Planck units and

exactly

can be either black or white, then the surface of the screen encodes

all

the information that region of space contains.

Of

course this

is all

very counterintuitive.

amount of information X, and region B

contains

If

region

A

contains

amount of informa-

tion 7, then surely joining the regions should give us a storage capacity X-l-

7?

this.

But Bekenstein’s bound

For example, a cube

1

tells

us that the

sum

is

less

10^^ bits;

but a crate

containing a million of those cubes can store only

1

meter on a side

10^®, rather

than

Where did all the extra capacity go? I have heard van ’t Hooft,

among others, admit that he

finds

it

very baffling.

But suppose that the universe does consist of information 1

Bekenstein’s rule

would seem

bit

at a

per cubic Planck unit at the finest scale, as

density of about

evolves via local interactions.

erything

than

centimeter on a side, the size of a sugar

lump, can store approximately

10^2, bits.

always

we know about

and

that this information

What would we

expect to observe? Ev-

to imply,

the laws of physics gives us a strong hint that

the rules of the Planck-scale interactions will be reversible, at least to a

good approximation: There %will be no

intrinsic

arrow of time. This

we cannot possibly expect to store or retrieve information at this scale: The bits will be flickering from one value to another much means

that

Proving and Improving Many-Worlds / 247

too unpredictably. They would represent a kind of subinformation

we would not expect

that

We would

expect stable patterns

used by IGUSes

as

and read

—

to be able to access directly.

like ourselves,

—

accessible bits of information

which can be written, j*^embered,

to exist at best as correlations

between the Planck-level

Figures 15-2 and 15-3 give us a crude visualization:

The

bits.

pixels printed

on each

side of the paper represent subinformation, but the pattern

which

revealed by the process of comparing

is

them

(in this case

when

held up to the light) contains “real” information. Note that

the page

is

this real

information

is

being stored nonlocally: You could

page in two with a sharp razor and take the two sides

slice

far apart;

the

then

the real information could not be said to be contained in either piece

on

its

own, but

If there is

it is still

present.

anything to

not just two but

my speculation, in

reality

column of

usually goes unnoticed: the

typical stairwell.

probably takes

many bits of subinformation to store one bit of “real”

information. A better metaphor will be familiar to it

it

all

readers, although

light switches

found on a

Using a simple trick invented by the Victorians (no

modern electronics is required) the switches are wired up in such a way that toggling the switch on any floor switches the light at the top between on and off, irrespective of the current positions of the switches on all the other floors. Here the position of the switch on each

floor,

the light,

up or down, represents

on or

off,

represents

1

1

bit

bit

of

of subinformation; the state of

real information, a

property of

the whole system.

Now let

us return to the multiverse picture. If a multiverse-com-

puter has a storage capacity of

1

bit per cubic

Planck unit, and sup-

we have dubbed worlds can make independent

ports a multiplicity of the reasonably stable entities local worlds, obviously not all of the

use of the same storage.

A problem will arise rather like that of sharing

amount of radio waveband between different users; the more transmitters, the more unavoidable cross-talk there is as each extra user contributes to the general background of noise. The amount of a finite

multiverse-information a region of space can store does indeed increase with the cube of its linear dimension, but

if

the

number of stable

processes in which that region participates also increases

portion to

its

—

say, in

pro-

linear dimension, the time light takes to cross the re-

248 / Schrodingers Rabbits %

gion

—then

that explains

why its

available information storage capac-

from the point of view of any one world process, increases only with the square of th^ dimension, just as we observe. Perhaps a cube ity,

10 100 Planck units

a side can indeed store about 10^^® bits of

on

subinformation or multiverse information', but

be

this capacity has to

divided between 10^®° world processes, giving by simple division only 10^®° bits

of stable “real” information capacity available to each.

emphasize that

I

very speculative thor in the

last

—

I

of a hidden-variable multiverse

this picture

is

taking the license traditionally allowed an au-

am

chapter of a science

book

to

its limits!

But the picture

would enshrine our familiar three dimensions of space and one of time as the reality to which

has

we took

temptations. If

its

Hilbert space

is

a

seriously,

it

mere approximation, abolishing the unwanted mul-

titudes of extra states that can be derived

And my

it

speculation

not quite so wild as

is

concept of subinformation

from Hilbert

is

not new.

it

space.

may

The

appear.

Quantum has always seemed to

imply that the universe somehow “knows” more behind-the-scenes information than can be measured in any one world line. For example, consider a simple polarizing

quantum

entity, a

photon that has passed through

38.123456789 degrees to the horizontal.

filter set at

bit

subsequent polarization

But there

verse seems to

know

cause the photon later

not

only

if

is

is

also set at precisely

which the uni-

more

exactly, be-

filter it

encounters

38.123456789 degrees, and

any other angle.

at

tween

this

However,

I

may

way of looking

am

also recognize a certain relationship beat things

more fundamental

atoms

Ilya Prigogine.

argument, which

is

essen-

notably the thermodynamics of gases,

it

to think of matter as a process than as a set of

in specific positions, because

is

and the work of

really reversing Prigogine’s

tially that in certain contexts,

tions

a sense in

the angle of polarization far

(Physicist readers

is

is

certain to pass through a second

that filter

ex-

of information about the photon’s

perimenter can only read one state.

An

a

fundamental to

the; gas

our ignorance of the atoms’ posi-

having the properties

it

does.

I

am

suggesting that

regard Planck-level subinformation as be-

ing as real as

cbnsider atoms to be, even though

never read

it

we should we normally

directly.)

we can

Proving and Improving Many- Worlds / 249

Let us be clear.

The

quantum mechanics;

picture

am

I

I

am proposing differs from

replacing the putatively infinite measures

of worlds depicted in Figure 12-lc with something more

which huge but

ture of 12- lb, in

orthodox

finite ratios

like the pic-

of numbers of different

worlds reproduce (to an extremely close approximation) the outcome

by orthodox quantum mechanics. But

probabilities predicted

this

is

not some wild defiance of Occam’s razor. In January 2004, just months before

wrote

I

David Deutsch published a thought-pro-

this chapter,

voking paper entitled “Qubit Field Theory”® in which he demonstrated that conventional

quantum mechanics

mation that can be described

places

no

limit

on the

infor-

Quantum

in a limited region of space.

mechanics must be modified to cope with Bekenstein’s bound.

would

I

like to

propose a program to see

variable multiverse theory straints

and

details.

The

is

first

if

such a hidden-local-

indeed possible, and flesh out

stage in such a project

might be

its

con-

to write a

simple computer algorithm or model that makes use of the following suggestions:

It

1.

must follow

a simple deterministic update rule, with the

state

of each Planck volume of space (probably represented by a single

pixel

on the screen) changing each time

only by

its

own

state

way determined

and that of its immediate neighbors.

The updating must

2.

step in a local

give rise to an ever-growing multiplicity

of divergent stable patterns that interact significantly with their “worlds” but

made

little

with divergent ones. Different world lines should be

distinguishable to the eye by appropriate use of color

haps flashing pixels 3.

Make

it

and per-

at different rates.

possible for a pattern to give rise to a large

number of

“daughter” patterns as the result of a single branching event; the tive

numbers of the daughter patterns should conform

analogous to the Born 4.

creasing

own

to

rela-

something

rule.

Consider the following mechanism for “condensing” an in-

number of

stable patterns

centirneter cube containing a given

Planck lengths on a creases each side

side.

from time-symmetric

rules.

number of particles

about

is

A

1-

10^^

Every second, cosmological expansion in-

by about

10^^

Planck lengths, vastly increasing the

250 / Schrodingers Rabbits X

amount of information about the

particles that

we can know from one

particular universe viewpoint.

^

As Penrose h^s pointed

5.

out, space-time should curve differ-

move

ently as perceived in different world-lines as masses positions.

The presence of a large amount of nearby mass should make

local processes

flows

to different

proceed more slowly in a given world-line, because time

more slowly

in a gravity well.

Can

the

model

replicate these ef-

fects?

Feel free to check

my Web

site for

any progress on

this

program:

http://www.colinbruce.org.

If

we turn out

to live in

such a comprehensible place as a

multiverse of hidden local variables obeying classically deterministic rules

—which

in

my

highly personal opinion would be the ultimate

extrapolation of the Oxford Interpretation

—

things will arguably have

turned out the best we could have hoped for in

enough

will inhabit a universe strange

all

possible worlds.

to fascinate, yet

We

one capable of

being visualized with our simple ape brains, run by a clockwork that scientists

of the past such as Newton and Laplace would have under-

we can hope

stood, a universe in which

to play tick-tack-toe with the

'

gods.

We

might even be able

find our-

could perform thousands of calculations in parallel using no

more hardware than required slight difference in the laws

for a single conventional computer, so a

of physics could make the difference be-

tween a universe that can run only one world that can

run a colossal number.

efficient use

is it

If a

line

and a multiverse

multiverse represents a vastly

more

of resources, in terms of the number of intelligent species

or individual beings

then

why we

such a universe. Just as the optical-fiber computer we met

selves in earlier

to explain definitively

not

it

can contain per unit of information processed,

statistically

almost inevitable that

we

find ourselves in

such a place?^

But

now I am treading very close to

from metaphysics, and

it is

the line that separates physics

definitely time to bring this

book to a close.

APPENDIX

THE PRINCIPAL PUZZLES

OF QUANTUM

PPQ

1

Spooky quantum

links

nals or that local events

way

at

PPQ

each end of the

seem

imply either faster-than-light

to

do not promptly proceed

in

sig-

an unambiguous

link.

2

Spooky quantum nals or that

PPQ

'

quantum

links

seem

to

imply either faster-than-light

sig-

events are truly random.

3

Why

does the universe seem to waste such a colossal amount of

effort investigating

pened but

might-have-beens, things that could have hap-

didn’t?

PPQ 4 Why tern,

does reality appear to be the world in a single specific pat-

when

the guide waves should be weaving an ever

multiplicity of patterns?

251

more tangled

V

f

*

Xi V*

i

I

N

NOTES '4

Chapter 2 1.

By the time Compton did

the expected result. Einstein

won

his experiments in 1923, this

his first

Nobel Prize

the related photoelectric effect, explaining the are

knocked from

formed the

first

solid materials

was

for describing

way individual electrons

by individual photons. Planck per-

photon

theoretical calculations of

momentum and

energy, although he did not take his hypothetical photons seriously. 2.

A more

advanced mental picture

I

like to use,

both the surfer and the wave in a single system,

Mobius band, has

a twist in

stretchable material but

some

elastic

is

energy in the

it.

is

a

which catches

hoop which, like

Imagine that the hoop

is

made of very

resistant to being twisted, so that

twist.

The twist

is

a

it

stores

not uniformly distributed

round the hoop. At any given point, the degree of twisting corresponds to the amplitude of the wave.

point

— most

twists

itself,

likely

somewhere the

later,

the ring snaps at

local twisting

is

greatest

in

elastic energy.

some

—and un-

reforming as a simple hoop, no longer a Mobius

no longer storing any works only

Sooner or

strip,

and

The hoop-with-twist metaphor

two dimensions, but physics-knowledgeable readers can

think in terms not of a Mobius strip but a skyrmion, a corresponding

kind of topological knot in three-dimensional space.

253

254 / Schrodingers Rabbits \

1.

Chapter 3 For example,

the electron detector

if

that has a current induced ip

nearby,

cause

it still

has

some

effect

it onl)j^

on

its

when

tiny, fluctuating

magnetic

a passive loop of wire

a charged particle passes

neighborhood

random thermal motions of electrons

duce a

is

at

other times, be-

m the wire loop will pro-

field.

Chapter 5 Including more-sophisticated experiments involving three

1.

particles rather than two,

whose

results are

even harder to quibble

with.

Howard, D. 2003.

2.

A

tion?

Who

invented the Copenhagen Interpreta-

study in mythology. Available

at:

http://www.nd.edu/

-dhoward 1 /Copenhagen%20Myth%20A.pdf Bohm, D., and B. J. Hiley. 1993. The Undivided 3.

Universe.

New

York: Routledge. Price,

4.

H. 1996. Time's Arrow and Archimedes' Point:

rections for the Physics of Time. Oxford:

constraint in our future

Oxford University

would probably be

different

constraint in the past, the pointlike Big Bang.

micro order^rather than macro order.

clump of seaweed

at

low

tide.

A

It

New Di-

Press.

The

from the known

would be

visual analogue

At the seabed the strands

a state of

would be

all start at

a

the

same point (macro order, the Big Bang); at the surface the strands are spread apart, but wind and buoyancy force them to lie exactly parallel to

one another (micro order). For example, the existence of particle interactions that exhibit

5.

what

is

called

CPT

violation are a

problem

stands for charge-parity-time violation. in a fully

The

for Price’s version. This particles

do not behave

time-symmetric manner.

Chapter 6 1.

There are many possible quibbles with the exact

mologists can

feel free to

add

a

few orders of magnitude.

figure.

Cos-

Notes / 255 2.

Joos, E. 1999.

Elements of eilvironmental decoherence. In

P.

Blanchard, D. Giulini, E. Joos, C. Kiefer, and I.-O. Stamatescu (eds).

Decoherence: Theoretical, Experimental, and Conceptual Programs. Heidelberg, Germany: Springer.

'4

Chapter 8 1.

See www.lhup.edu/~dsimanek/fe-scidi.htm.

2.

Russell,

Modern 3.

B. 1991. Inventing the Flat Earth:

J.

Historians.

New York:

Gribbin,

2002. Science:

J.

Columbus and

Praeger.

A

History 1543-2001. London: Pen-

guin Books, pp. 421-424.

Hoping

4.

that

cause their influence

you can ignore the is

relatively small

example, the inverse-square law

tells

is

you

effects

of far-off things be-

not necessarily justified. For that

many forces diminish by

a factor of four for a doubling of distance, but a doubling of distance

implies that you

must then take

into account the effects of objects in

an eightfold greater volume of space.

you can

If the

action

is

instantaneous,

get the kind of self-reinforcing interactions that

call positive

feedback. There

is

we nowadays

never a guarantee that the universe will

be comprehensible, but a universe incorporating instantaneous longrange interactions

is

Turnbull, C.

5.

likely to

M.

be almost impossible to get to grips with.

1961. The Forest People.

New York: Simon

8c

Schuster, quoted in R. D. Gross. 1987. Psychology, the Science of Mind

and Behaviour. London: Hodder Claire

Chambers

for tracking

8c

Stoughton,

down

p. 129.

1

am indebted to

the source of this story.

Chapter 9 1.

tangled

Deutsch, D., and

quantum

P.

Hayden. 2000. Information flow

systems. Centre for

in en-

Quantum Computation, The

Clarendon Laboratory, University of Oxford. Proceedings of the Royal Society of London, Ser. 2.

A 456:1759-1774.

Tegmark, M. 2003.

Scientific American,

May. An expanded ver-

sion appears in the online physics archive http://www.arxiv.org.

1

256 / Schrbdingers Rabbits

Chapter 10 Kwiat, Zeiliger et

1.

measurements

effect,

quantum

interrogation

arXiv:quant-ph/9909083

X

"

Paul, H.,

High-efficiency

quantum Zeno

via the

vl 27 Sep 1999. 2.

al.,

and M.

Pavicic. 1997. Nonclassical interaction-free

detection of objects in a monolithic total-internal-reflection resonator.

Journal of the Optical Society of America B 14:1273-1277. Kent, A., and D. Wallace.

3.

Quantum

X-ray.

Quantum interrogation and the safer

Physics, abstract quant-ph/01021 18 vl.

Chapter Feynman,

1.

1

R. 1982. Simulating physics with computers. Inter-

national Journal of Theoretical Physics 21 (6/7):467-488.

Deutsch, D. 1985.

2.

Quantum

theory, the Church-Turing prin-

and the universal quantum computer. Proceedings of the Royal

ciple,

Society of London, Ser.

A 400:97-1 17.

3.

http://www.chem.ox.ac.uk/curecancer.html.

4.

http://www.climateprediction.net/index.php.

5.

Other discoveries such

require further

as Grover’s search

work before they can

algorithm

truly be said to

still

do anything

“useful.”

Chapter 12 Vaidman,

1.

L.

2002.

“Many- worlds

interpretation of

quantum

mechanics.” In E. N. Zalta {ed.),The Stanford Encyclopedia of Philoso-

phy (Summer

ed.). Available at: http://plato.stanford.edu/archives/

sum2002/entries/qm-manyworlds/. Deutsch, D. 1985.

2.

ciple

theory, the Church-Turing prin-

and the universal quantum computer. Proceedings of

Society of London, Ser.

tangled

A

quantum

P.

Hayden. 2000. Information flow in en-

systems. Proceedings of the Royal Society of London,

456:1759-1774. Available

9906007.

the Royal

A 400:97- 117.

Deutsch, D., and

3.

Ser.

Quantum

at:

http://xxx.lanl.gov/abs/quant-ph/

Notes / 257

Deutsch, D. 2004. Qubit fiel5 theory, January. Available

4.

at:

http://arxiv.Org/ftp/quant-ph/papers/0401/0401024.pdf. Wallace, D. 2003. Everettian rationality: Defending Deutsch’s

5.

approach to probability in the Everett interpretation. ics,

abstract quant-ph/0303050 revised

Another notable

6.

his discovery that

British

an ecosystem

March

example

is

is

it.

Phys-

^ ^

11.

Jim Lovelock, famous for

unstable until

the chemical resources available to

Quantum

it

becomes limited by

A consequence is that the atmo-

sphere of any life-bearing planet should deviate from chemical equilibrium, so planets with ecosystems should be detectable from afar by

looking for excesses of such gases as ozone and methane. Lovelock’s

concept of “Gaia” to describe the Earth’s dynamic equilibrium

him

a darling of the early

patents 7.

made

eco-movement. His income from ingenious

made an academic post unnecessary. Barbour’s more technical work, which

is

too complex for us

go into here, essentially concerns the problem of how we can specify the state of the whole universe at a particular instant when, due to

to

relativity, different

multaneous 8.

observers do not agree on what constitutes a

si-

instant.

Gell-Mann, M. and

H. Feng and B.-L.

Hu

J.

B. Hartle

“Strong Decoherence” In D.-

(eds). Proceedings of the 4th Drexel Conference

on

Quantum Non-Integrability: The Quantum-Classical Correspondence. Hong Kong: International Press of Boston. arXiv:gr-qc/9509054 v4 23 (Nov).

Chapter 13 1

.

2.

http://www.hep.upenn.edu/~max/index.html. Lewis, D. 2004.

How many

lives

has Schrodinger’s cat?

Australasian Journal of Philosophy 82:3-22. 3.

In the full

Gulliver's Travels^

plight of these

and nightmarish version of Jonathan

which

is

Swift’s

not normally given to children to read, the

immortal but

terribly enfeebled

and

senile persons

is

graphically described. 4.

2004.

Sebastian Sequoia-Jones, conversation with the author,

March

258 / Schrodingers Rabbits

5.

David Wallace, conversation with the author, November 2003.

6.

Piccione, M.,

and A. Rubinstein. 1997.

of decision problems with imperfect "

havior 20:3-24.

‘

recall.

the interpretation

Games and Economic Be-

Vx

Vaidman, L. 200 1 Probability and the

7.

On

.

MWI. In A. Khrennikov

%

Quantum

(ed.).

Theory: Reconsideration of Foundations. Vaxjo, Swe-

den: Vaxjo University Press, pp. 407-422.

Chapter 14 1

Penrose, R.

.

1

989. The Emperor's

New Mind. New York: Oxford

University Press.

Marshall W., C. Simon, R. Penrose, and D. Bouwmeester. 2002.

2.

Towards quantum superpositions of a mirror. Quantum Physics, abquant-ph/02 10001, revised September 30.

stract

Chapter 15 1

To a many-worlder like myself, this “tip-of-the-iceberg-effect,”

.

the discrepancy between the large

know about

verse needs to

make

it

amount of information that the

the particle (the exact angle of

behave appropriately, and the single

bit that

its

uni-

spin) to

can be read out in

any given “wprld,” can be seen as further evidence for the existence of the multiverse.

For further discussion of this lattice-based approach, includ-

2.

ing a description of Planck lengths and the holographic principle, see

Chapter 3.

16.

Normal

tolerances in the process of printing, folding,

binding these book pages

may result

in

and

an inexact superimposition of

Figures 15-2 and 15-3, thus preventing the stated effect from occurring.

To observe

them back

to

it,

the reader

may photocopy both

back against a strong

light,

figures

and hold

adjusting the superimposi-

tion carefully until the effect appears. 4.

Many readers will hava realized that this is just a variant of the

one-time-pad 5.

native

still

used for sending secure messages today.

Zeilinger has attempted to develop his system using an alter-

measure of information

to that given

by conventional Shannon

Notes / 259

information theory.

He believes that this approach

is

justified

because

the classical “ignorance” interpretation of probability described in

Chapter 5 claim

is

is

not adequate in a

vigorously disputed by

quantum

context.

The

validity of this

many theorists.

'4

Chapter 16 Shahriar, A. 2004.

1.

“Quantum

Rebel.”

New

Scientist^ July 24,

p. 30.

2004,

Plaga, R.

2.

1

997. “Proposal for an experimental test of the

many-

worlds interpretation of quantum mechanics” Found.Phys. 27 559. http://xxx.lanl.gOv/PS_cache/quant-ph/pdf/9510/9510007.pdf.

Vaidman,

3.

tron,

L. 1996.

On

schizophrenic experiences of the neu-

Quantum Pysics, abstract quant-ph/9609006, revised September

7.

Tegmark, M. Does the universe in

4.

fact

contain almost no in-

formation? Foundations of Physics Letters 9:25-42. This statement of course needs qualifications. For example,

5.

if

the galaxies involved contain not just pointlike stars but clouds of gas

and

dust, as

tions

most or

between those

and other

effects.

classical physics

all

galaxies do, there will be significant interac-

entities that

But the point

Feynman,

Modern

Mass.:

R. 1994.

little

make is that perfectly share the same volume of

trying to

with one another.

The Character of Physical Law, Cambridge,

Library.

Bekenstein,

7.

am

I

can include things that

space, but interact relatively 6.

can trigger bursts of star formation

J.

D. 1973. Black holes

and entropy. Physics Re-

view 07:2333-2346. Deutsch, D. 2004. Qubit

8.

field theory, January. Available at

http://arxiv.Org/ftp/quant-ph/papers/0401/0401024.pdf 9.

We

could take this anthropic argument a step further.

One

of

Oxford’s most famous authors, C.S. Lewis, speculated that the vastness of cosmic distances might represent “God’s quarantine regulations,”

extend false:

ensuring that an imperfect species such as our its

influence to other worlds.

Travel over interplanetary

own

We now know that

and even

his

could not

hope was

interstellar distances

is

defi-

260 / Schrodinger's Rabbits \

nitely possible for a technologically

mers wondering how many

is

what

normally only one queen

new queen

species. Indeed, astrono-

intelligent species

tain have seriously cons^idered

There

advanced

is

called the

iia.a

our universe

their larval cells.

might well use

An

its

con-

Queen Bee hypothesis.

hive of bees, because the

be born promptly stings any potential

to

may

rivals to

first

death in

intelligent species that develops interstellar travel

power

similarly to ensure that

any dangerous competitors. In that

it

would never have

case, there will usually

be only one

intelligent species per universe.

The same logic would apply to the multiverse was any way

at all in

as a

whole

which creatures occupying one small

—

there

if

slice

of

it

could reach out to affect other “parallel worlds.” For a multiverse to

support a huge number of species, we do not need merely laws of physics that efficiently support multiple processes. a very special

subtle

combination of properties, for they must

way make

it

not just technologically

tally impossible, for a being,

fect

world

They must embody

lines far

however

removed from

currently discovering.

its

difficult,

also in

some

but fundamen-

intelligent, to systematically af-

own. That

is

exactly

what we

are

INDEX ' 4

A

Backward-in-time causation, 71, 72-73

Acoustically driven optical switches, 212

Action

at a distance, 47-48,

signaling, 8-9, 10, 31-32, 36, 40, 42,

113-115,

44,47-48,51,52,206

117-118, 123, 222

travel,

45

Adams, Scott, 160-161 Adams, Douglas, 179

Bambuti pygmies, 121

Afshar, Shahviar, 230

Baroque quantity of calculations, 53 Bekenstein, Jacob, 246 Bekenstein limit, 87, 176, 246, 249

Barbour, Julian, 178-181, 257

Air molecules, localization time, 85 Aliens, 9, 11, 44

game-playing, 94-102

Bell,

SETl

Bell- Aspect

project, 158

Andromeda

galaxy, 50

226, 236-237

Anthropic principle, 183 Artificial intelligence,

Bell’s inequality,

208

Binary

Aspect experiment 15, 22-23, 55, 58, 80, 1

36-37, 225-226

Big Bang, 139, 254

Aspect, Alain, 33, 62. See also Bell-

Australia, 8, 41-42,

experiment, 34-39, 41, 49,

51,62, 89,206,212,221,225,

Angstrom, 19

Atoms,

John, 32, 36, 69

calculation, 159-160

126-127

digits, see Bits

12

message, 221

Birkbeck College, 69, 73, 201 Bits, 52, 88, 89,

B

156,216, 243

Black holes, 200, 201, 216, 246 Bletchley Park, 162-163

Babies, expectations of physical laws,

Bloch sphere, 88-89, 166

107-110, 112, 114, 118

261

V

262 / Index

Bohm, David,

32, 69-71, 73, 88-89, 133,

Collapse, 178, 212

143, 199, 201

Bohmian mechanics,

Coleman, Sidney, 206 conscious ob^^erver hypothesis, 68-

70-71, 236

Bohr, Niels, 63-67

69,

207

^

Book-writing program, 238-239-\

by decoherence, 83-84, 203, 205

Bomb

entropy and, 68

detectors, 142-153, 174, 204

Borel, Emile, 50, 83

environmentally induced, 84, 133

Born, Max, 61

by

Born

rule, 61-63, 178,

gravity,

201-206

GRW-based mechahisms, 198-210

249

Hilbert space, 80, 82, 83-84, 138,

Bose-Einstein condensate, 70

161, 162

Branching of probabilities, 170-173,

instantaneous, 12, 31, 71

176-178, 179

mind, 207-210

Brown, Harvey, 169, 184 Brownian motion, 26, 189, 191

in

Buchan, John, 148

phase change metaphor, 30-31

Buckyballs, 86-87, 211-212,213

probability, 199

Butterfield, Jeremy, 169

times, 67-68, 203

nonlocal case, 58, 69, 206

Color, 15,21-22, 180

Butterfly effect, 50, 158, 159, 235

Colossus computer, 162-163

Columbus, Christopher, 44, 113 Communication between worlds,

c

7-9,

137-138, 140-154, 229, 233-236. California Institute of Technology, 206 Carroll, Lewis. See

See also Faster-than-light

Dodgson, Charles

Cat's Cradle, 30-31

signaling

backward-in-time, 8-9, 10, 31-32,

Cat-box experiments, 59, 68-69 Causality, 51, 65, 71, 72-73, 153,

36, 40, 42, 44, 47-48, 51, 52,

226

Cellular

Compton

Compton, Arthur,

automaton,

1

18-119, 243

Computers. See

models, 24'3-244

Centre for

Quantum Computation,

169, 176

effects, 50,

Classical

behavior of photons, 20, 23, 26, 28 physics, 36, 47, 55, 65, 106-111, 207

systems, 80 theories, 57-73

also

253

Quantum

computers/computing analog, 155-157, 168

Climate Prediction Project, 158-159 Clocks, 45, 110, 121

Co-probability patterns, 83 breaking, 97-98, 161-165, 218

168

information storage, 216 optical, 135,

240-242,250

parallel processing,

157-159

Turning machines, 207, 208, 210

Condensed matter

physics, 168

Consciousness, 191, 199,207-210

Conscious observer. See also Observer

universe, 61, 75, 139, 179, 213-214

Cold fusion, 168

15, 21,

digital, 156, 157,

55-56, 175, 186-187

Churchill, Winston, 183-184

Code

18-21

Colossus, 162-163

CERN, 32 Chaos

effect, 15,

206

effects

experiment, 229-230 Consistent histories in

many-worlds, 126, 127, 129, 131, 133, 175, 180, 181-182

tendril metaphor, 131

Index / 263

Detectors, 48, 50. See also

Context dependence, 84

Continuous universe, information

Measurement

infinity of

in,

213, 214-216,

bar-code scanner, 53

bomb, 142-153,

243

effect

174, 204

53-54

Conway, John, 243, 244 Copenhagen interpretation, 63-67, 132-133,152,230

environmental

Copernican principle of mediocrity,

polarizing

filters,

in two-slit

experiment, 27-28

137, 182

effect,

interaction-free,

\

1

54

radiation, 127

32-33, 40, 49

Deutsch, David, 70, 89, 130, 147, 155,

Copernicus, 104

157, 159, 165, 169, 170, 174,

Correlations angles of polarization, 34-35

175-178, 184, 190, 196, 197,200,

lottery cards, 7-9

229, 230, 236, 240, 249

Deutsch-Wallace program, 178

nonlocal, 220, 221

Cosmic background radiation, 85-86 Cosmic expansion, 69, 139, 249-250

Dice, 6, 9, 53

CPT violation,

Dilbert space, 165

254

Dilbert Hotel, 159-162

Cultural relativism, 100-102, 121, 200

Dimensions of many-worlds, 171-172,

Cushing, James, 240

181

Cramer, John, 72-73

179,

of Hilbert space, 87-89, 181 Disch, Thomas, 192

D

Discontinuous function, 164-165 Disorder, 71-72

Damping time, 86 DARPA, 52

Distributed information, 217-222

Davies, Paul, 136

Domino

effect,

56

de Broglie, Louis, 62, 70 de Witt, Bryce, 134, 135

Doppler

effect,

122-123

Dowker,

Fay, 182, 183

Decision theory, 177

Du

Dodgson, Charles, 45

Fay, Charles, 114

Decoherence collapse by, 83-84, 203, 205

E

and entropy, 86 environmentally induced, 53-54, 86, Earth, 8, 34, 42

129

curvature, 111-113, 123

experiments, 86-87

macroscopic

effects, 175,

and many-worlds,

182

126, 127, 128,

epicycle paradigm, 102-103

ether wind, 120

129,132,133-134,138,175-177,

position of stars relative

178, 182, 236

potential states, 55-56

strong

vs.

testing,

weak, 182, 230

85-86

to,

136

relocalization, 85

Earth Simulator supercomputer, 157

time, 85, 86

Echo Round His Bones, 192

turbulence analogy, 66

Einstein, Albert, 6, 7, 12,31 -32, 53, 56,

Delocalization, 85-86

62, 89, 103, 116, 120, 121, 128,

Dennett, Daniel, 127

253

1

S'.

264

Elitzur-Vaidman experiment, 140-144,

/ Index

Everett,

174, 228

Hugh,

133-134, 135, 138-

III,

139, 171, 184

Electromagnetic waves, 110, 116-117,

Expectations

119

knowledge and^ 60-6

Electrons, 9

Compton

of physical laws, 107-110, 112, 114,

^ effect, 15,

18-21

118

detector, 254

information encoded

in,

214-215

F

localization, 24

.

orbits/energy levels, 22-23 Factoring, 96, 161-162, 164-165

pointlike nature, 23

Faraday, Michael,

spin, 12, 32, 88, 166,214-215

and causality, 72, 153 and many- wo rids, 132,

magnetic, 116, 117

mass-energy

paradoxical consequences, 45-48,

52

Entanglement, 29-30, 206, 229, 242

and many- worlds,

quantum tunneling and,

126, 127, 166,

spooky

178 links, 31, 226,

links and, 7-8, 31-32, 38, 51,

Feynman, Richard, 71-72, 92-93, Fields

surfer analogy, 34

electrostatic,

Entropy, 68, 86, 246 effects.

1

14-1 15,

1

16,

1

17,

1,

116,201-206 local interactions, 123

of detectors, 53-54

magnetic, 51, 110, 114, 115, 116,

Epicycles, 102-105

117

paradox, 62, 90

quantum

experiment, 34-39, 41,

potential, 70-71

Fields Medal, 164

49,51

Fill-the-Gap, 98

local effects and, 130-132, 176

Finite

lottery card puzzle, 1-12, 36, 38, 61

dimensions of Hilbert space, 87-89

predestination and, 72

information storage and

surfer analogy, 31-32

retrieval,

87

Error correction, 87, 165

Fitzgerald, George, 117

C., 199

Leonhard, 119-120

10,

gravitational, 50, 82-83, 110-11

collapse induced by, 84, 133

Ether wind, 120-121, 245

1

165

See also

Decoherence

Event horizon, 246

155,

168, 242-243

of states, 83-84

Euler,

90-91, 228

53-54, 58, 62, 129

229

qubits, 166

M.

176, 184,

206

relation, 103

Enigma code, 163

Escher,

18,

236-237

gravitational, 201, 203

Bell- Aspect

1

Bell-Aspect experiment, 34-38, 62,

flows, 68

EPR

17,

1

Faster-than-light signaling, 40, 42

wave behavior, 23-24 Energy

Environmental

14-1 16,

128

two-slit experiment, 23, 25

spooky

1

Fleischmann, Martin, 168 ^

Fluid dynamics, 66, 80, 118-119 Flux, 117,201 Flat earth hypothesis,

111-113

Index / 265

Fourier analysis, 104 Free will, 9

Hamlet, 237-238, 239

Freezing metaphor, 30-31, 56 Friction, 86, 103, 110,

1

Hartle, James, 181-183

13

Harvard University, 206

Hawking, Stephen, 23,^00, 205, 246 Hawking radiation, 216

G

Hayden, Patrick, 130 Galaxies, 136-137, 139 colliding, 241-242,

Heaviside, Oliver, 117

259

Heisenberg, Werner, 25-26, 31, 64, 65,

Galileo, 104

Game

90

theory, 93

High-finesse cavity experiment, 41,

Games theory, 92-102 Gamma-ray photons, 204

204-205

Hidden

Gardner, Martin, 214

Gaze

test,

local variables, 26, 38, 62, 72,

240, 242, 243-244, 245-250

108

Hilbert, David, 74, 160, 208

Gell-Mann, Murray, 181-183, 230

Hilbert hotel, 160-161, 208

Ghiradi, G. C., 198

Hilbert space, 74, 208

Gilbert, William,

cat-box experiment, 81-83

14

1

Glashow, Sheldon, 206

collapse, 80, 82, 83-84, 138, 161, 162

Gods-playing-games metaphor, 92, 94-

computing

102, 184

159-162, 165, 166

in,

and context dependence, 84

Godel, Kurt, 208

density, 80

Godel’s theorem, 210

dimensional requirements, 87-89,

Gravitational

181,248

201-206

collapse,

many-worlds interpretations,

84,

constant, 245

126-127, 129, 133, 137, 138, 178-

energy, 201, 203

184

field,

50, 82-83, 110-111,112-113,

114, 123

quantum tunneling and, 90-91

181-182

probability waves, 75, 77-80, 87, 90-

GRW-based mechanisms, 198-210 Guide waves, 202. See circular,

also Pilot

waves

29

91, 126-127, 133

real-space relationships, 90 Hiley, Basil, 71

disruption by detector, 53, 142 epicycles

effect in, 130, 138,

162

interactions, 241-242 Griffiths, Robert,

measurement

compared, 105

and faster-than-light signaling, 38 hologram analogy, 54 and many- worlds, 128

History

lines,

127

Holistic

behavior, 51

property of neurons in consciousness, 191

packets, 150-151, 152

Holographic principle, 246

phantom quantum

Holograms, 48-49, 54

field,

62

potential, 70-71

for solid objects, 24

surfer analogy, 21, 24, 25-26, 34,

150-151

Hooke, Robert, 1 14 Howard, Don, 64-65, 67

Human Genome Project, 158 Human Proteome Project, 158

s

266

/ Index

Interpretations of theories, 100-102,

I

115

\

Ignorance interpretation, 60-61, 195,

Intuition, as quarv^um

258

210

'

IGUSes, 183, 191-192,247-

^

Immortality, 189-192

I^yerse-square rule, 115, 255 Isolated systems, 118, 126-128

Implicate order, 71 Inferential

computing, 208-

\

knowledge, 64

measurement

effect,

j

28-29, 31, 39

Infinity, 58, 67, 77, 114, 170-172, 175,

Joos, Erich, 85

176, 197, 201

of information, 213, 214-216, 238

Information

encoded

infinity of, 213, 214-216,

238

Kent, Adrian, 154, 182, 183

interpretation of, 216-217

Kepler, Johannes, 104

nonlocal, 217-222

qubits

K

214-215

in electron spin,

Knowledge,

10, 60-61, 88, 166, 175; see

176

of, 89, 166,

also Inferential

sharing between worlds, 138, 233-

knowledge

Krakatoa argument, 196-197

234 storage and retrieval limits, 87, 216,

243-244, 245-249

L

Informational Principle, 217, 222-226 Infrared photons, 213

Laplace, 250

Instantaneous

Lattice model,

collapse, 12, 31, 71

Lawrence, Sarah, 176

everywhere-to-everywhere

links,

72

gravitational effect, 114

long-range interactions,

242-250

Lewis, C.

S.,

138, 259

Lewis David, 189, 190 1

18,

255

Life,

signaling, 8, 34, 45-46

game

of,

243, 244

Light. See also

Interaction-free detectors, 150-154,

density

228

of,

Photons 19

Faraday’s theory, 116

Interactions. See also

Entanglement

medium, 119-121

of particles, 29, 33, 34, 51, 54-55

pressure of, 15

of outcome worlds, 134, 178

speed

and probability wave, 78-79

of, 19, 42,

1

10, 117, 120, 121,

245

self-amplifying feedback, 118

two-slit experiment, 13

and

wave-particle paradox, 13-15, 15, 18

spatial localizations,

85

Interference, 14, 23, 24-25, 29, 48-49,

Local

82,86, 127, 129, 134, 143, 144,

cellular

149-150, 205, 213, 222-224, 230

conditions, 51, 52, 112-113

International Date Line, 45

interactions, 85, 109, 117, 123,

Internet

«

distributed projects, 157-159 security,

automaton, 118-119

132, 176, 184 stories,

163-165

«

\

240

universe, 240-242

BO-

Index / 267

Locality principle, 109, 113-114, 117,

^dimensions, 171-172, 179, 181

economy of assumptions,

118

and many-worlds, 128, 130-132,

entanglement and, 126, 127, 128, 132, 178, 206, 229

176, 184

experiments, 229-236, 249-250

proof of, 130-131 Localization, 24. See also Collapse

and

faster-than-lighlrinfluences,

132, 176, 184,

electrons, 24 spatial,

171

206

hidden-local-variable theory, 240,

85

242, 243-244, 245-250

time, 45, 85

Lockwood, Michael,

129, 192

Hilbert space and, 84, 126-127, 129,

Lodge, Oliver, 117

133,137,138,178,179,180-181,

Lorentz invariance, 206

182-183

Los Alamos National Laboratory, 163

information and resource sharing

between worlds, 138, 233-234

Lottery

card puzzle, 1-12, 36, 38, 41-42, 52,

interactions of outcome worlds, 134, 178, 205

69, 130-132, 148

and

chances of winning, 188

interference, 143, 144, 149-150,

205

tumbling cylinder, 50, 188

local interactions, 130-132, 176,

Lovelock, Jim, 257

184 multiplicity of worlds, 136-138,

M

170-171, 172,236

no-assumptions claim, 127-128

Mach-Zender interferometer, 141-144,

no-collapse interpretations, 127,

203-204

133, 190

Macro

opponents, 198-210,213

effects, 40, 50, 55-56, 67, 175, 182,

philosophical consequences

187-188,235

of,

185-

197

order, 254

PPQs

systems, 59

probability of outcomes, 126-127,

Magic square,

99,

227

133, 156, 157, 170-173, 174, 176-

Magnetic

178, 179-180-181, 184

energy, 116, 117 fields, 51, 110, 114, 115,

pressure,

and, 126-128

1

116

16

and randomness, 129-130 and special relativity, 132, 206 supporters, 132-133, 138-139, 169,

Mansouri, Reza, 206

174-183

Many-minds, 128-129

zero-probability outcomes, 134-135

Many-worlds Bohmian mechanics and, 70, 133 communication between worlds, interpretations

137-138, 140-154, 229, 233-236

Mars, 34, 42, 65 Marshall, William, 204-205

Mass-energy

Massive parallelism, 157, 159-162, 207-

consistent histories and, 126, 127, 131, 133, 175, 180, 181-182

decision theory and,

1

77

decoherence and, 126, 127, 128, 129, 132, 133-134, 138, 175-177, 178, 182, 236

relation, 103

208, 209-210

Max

Planck Institute, 232

Maxwell, James, 116, 117, 119, 120 Measure, Everettian, 171-173, 174, 176, 178

V S'. %

268

/ Index

Newtonian worldview, 113 NMR measurement, 41

Measurement with analog computers, 155 angle

of, 148,

Nobel

170

defined, 55-56

of distance to

prize, 164y,^46,

253

No-cloning theorem, 166

^

stars, 15*6

1^0-collapse interpretations, 127, 133,

“dialing in” metaphor, 229, 240

190

fundamental values, 249

Nonlocal information,^2 17-222

gaze time, 108

Nonlocality, 70, 71,

and

88-89 1

114, 143, 226.

See also Action af a distance

of internal properties of particles,

magnetic pressure,

72,*

collapse, 58, 69,

206

guide waves and, 62

16

of polarization, 32-33, 35, 212

Hilbert space and, 88-89, 90

zero-interaction, 153-154, 174

test of,

Measurement

effect, 12, 80,

34-39, 41, 49, 51, 62, 88-89,

206

228, 230.

See also Detectors; Observer

NP-complete problems, 166-167

effect

Nuclei, 15, 41, 201

amplification

of,

41-42

in classical world, 154

o

in Hilbert space, 130, 138

of inferential knowledge, 28-29, 31,

Observer

39

on

effects.

See also

Measurement

interference pattern, 24-25, 129,

EPR paradox;

effect

collapse hypothesis, 68-69, 207

143,205,222-224

Copenhagen

phase-change metaphor, 30-31

interpretation, 64-65,

67

surfer analogy, 28

quantum, 9-10,

Metaphysics, 250

25, 27, 38-39, 40,

58, 59

Michelson-Morley experiment, 120-

relativistic,

121

Occam’s

Might-have-be,ens, 54, 129

43-44, 110, 121-122

razor, 9, 39, 115, 127, 136, 226,

237, 249

Mind

Olympus,

collapse in, 207-210

Omnes, Roland, 181-182

information patterns, 128

Mobius

strip,

65, 94

Optical computer, 135, 240-241, 250

253

Oscillator,

Molecule, 85

Momentum, 15, 21-22, 113 Monolithic bomb detector,

decoherence time, 86

Oxford interpretation,

184,

250

Oxford University, 129, 132, 140, 169, 174, 176, 177, 199, 203,212

148-153,

228

Monopoly, 93-94

Monty

Hall problem, 60-61

p

Multiverse, 135, 168, 177, 178, 179, 180, 189, 192, 196, 197, 238, 239

Paradigms, flawed, 102-105, 111-113 Paradoxes of the absent-minded driver, 193

N Newton,

Isaac, 107,

1

randomness and, 52-53 14,

time

250

travel,

43

of Wigner’s friend, 68-69

%

Index / 269

jnomentum, 21-22

Parallax, 136 Parallel worlds, 138-139, 143, 155, 176,

monolithic resonator, 148-153 polarization, 12, 32-33, 88

233

surfer analogy, 28-29

Particles

collapse probability, 198

wave packets, 150-151, 152

behavior, 12, 13, 14, 25, 58

wavelength, 150

entanglement, 29-30

Pilot

in free space, 58 as knots in space-time, 243, lifetimes,

245

^

wave theory, 20-21^23-24, 70-71, 133, 143. See also Guide waves

Plaga, Rainer, 232-234

Planck, 253

24

internal properties, 88-89

Planck’s

constant, 21-22, 203, 245

Patterns

length, 217, 243,245

co-probability, 83

and cultural

subjectivity,

96-101

scale,

246

lottery cards, 5

Podolsky, Boris, 12, 31, 62

random, 217-219

Point-like

in reality, 127,

Big Bang, 254

128-129

two-slit experiment, 15, 17, 20, 23,

Pokemon, 94

222-224

Polarization, 12

Paul, Harry, 151-152, 228 Pavicic,

particles, 23, 58, 62, 75

angles of correlated pairs, 34-39

Mladen, 151-152, 228

32-33, 40, 49

Pearle, Philip, 198

filter,

Penrose, Roger, 133, 140, 169, 170, 199-

lottery cards as filters, 36, 38

measurement, 32-33,

210,250 Periodicity of a function, 164-165

qubit storage, 166

Personal identity, 185-197

rotator,

Permeability, 117

surfer analogy, 24, 32

Pons, Stanley, 168

Perspectives

Popper, Karl,

6,

64

Potential states, 55-56

PPQs, 40,51-56, 89,251-252

112 relativistic,

Phantom

field,

answers, 128-132

121-125

Predestination, 71-73, 184

62

Phase change, 30-31

Preferred basis, problem

Phlogiston, 102-103

Pressure

of,

181

of light, 15

Photons

bomb

212

144-147

Permittivity, 117

of physics, infant to adult, 107-111,

35,

detector detonator, 142-144

classical behavior, 20, 23, 26,

Compton

effect, 15,

28

18-21

magnetic, 116 Price,

Huw,

72, 73, 189,

254

Prigogine, Ilya, 248

density, 19

Prime numbers, 96, 161-162, 164, 165

discriminating between wavelike

Principal Puzzles of

and

particle-like behavior, 140-

144, 146-147

Quantum.

See

PPQs Probability

ghost, 152-153

of collapse, 199

guide waves, 24

branching, 170-173, 176-178, 179

localization time, 85

histories,

82

270 / Index

R

ignorance interpretation, 175, 195,

258 of many- worlds outcomes, 126-127,

Rabbits, 82

^

133, 156, 157, 170-173, 174, 176-

Radioheads, 241-242

178, 179- 180- 181,"184

Randi, James, 6

--

personal identity and, 193-196 rule of

Randomizing

U, 230-232

quantum, 61-63, 178

2

77-80

Randomness,

state space, 75,

transmission/reflection of photon,

waves, 61-63, 75, 77-80, 87, 90-91,

126-127, 133, 156, 157

51-53, 159

6, 13-14‘, 23,

distributed information, 217-219

spook

35-36

devices, 188, 195-196,

links and, 9,

1 1,

53-54, 129

Rational expectation. See Expectations

Recording of information,

8, 162,

240

110-111

Relativity,

epicycles and, 105

Q

general, 7, 87, 107,

1

16, 123, 200,

236, 246

Quantum

and

algorithm, 163-165 consciousness, 207-210

ion superposition experiment, 232-

234

locality,

123

special, 42-48, 62, 71, 103, 107,

1

16,

120-123, 132,206, 243 Relocalization, 85

Ripple, 19

potential, 70-71

effect,

29

roulette, 189, 197, 230-232 testing devices, 153-154

Rimini, A., 198

traditional interpretations, 57-73

Robertson, Howard, 206

tunneling, 90-91, 153, 228

Rohypnol, 193

Quantum computers/computing applications, 87, 147, 156, 163-165,

tank, 30-31

Rosen, Nathan, 12, 31, 62 Russell, Jeffrey, 113

166-168 architecture

and hardware, 165-166,

s

168, 176

centers for, 169 collapse of Hilbert space, 138

Saunders, Simon, 169, 184, 192, 195

error correction, 165, 166, 167

Schiaparelli, Giovanni,

human

Schrodinger, Erwin, 23

brain

as,

feasibility, 155,

207-210

230

information dissemination, 162 massively parallel processing, 157, 159-162, 209-210

65

Schrbdinger’s cat, 23, 59,

68-69, 73, 81, 83, 127,

232-234

wave equations, 58-59,

126, 132-133

operation, 138, 166

Screensaver programs, 157-159

qubits, 89, 166, 167

Screensaver- Lifesaver, 158

Shor’s algorithm, 163-165, 168

Self-amplifying feedback interactions,

Queen Bee

hypothesis, 259-260

Separation

Qubits, 89, 176

spacelike, 7,

entangled, 166 field theory, 176,

118,255

249

1

1,

41-42, 44

timelike, 44-45, 46-47

Index / 271 f

SETI@home

T

project, 158

Roman, 206 Shannon information Sexl,

theory, 258

Tegmark, Max, 132, 186, 188, 191, 230231,237, 238,239

Shor, Peter, 164 Shor’s algorithm, 163-165, 168

Teleportation, 229

Simulations, 162, 163, 215, 217

Tick-tack-toe analogiesf98-101, 180, 184,

probability wave, 90-91

quantum

processes, 80, 156, 167-

236

thought experiment, 42-

relativity

Skyrmion, 253 Sleeping Beauty problem, 193-196 sail,

travel, 45,

Trains

wave mechanics, 30

Solar

Time’s arrow, 67-68, 71, 72, 162, 179

Time

168

226-227,240

46, story,

15

206

64

Solar system, 104, 113, 120, 136

Transactional interpretation, 72-73

Solipsism, 10, 67

Transatlantic telegraph, 44-45

Spacecraft, 34, 43, 46, 75, 123-124

Traveling salesman problem, 166-167

Spin

Tree, decohering-worlds, 170-173, 177-

electron, 12, 32, 88, 166, 214-215

178

Tunneling

measurement, 88-89

network

phlogiston, 103

qubit storage, 166

quantum, 90-91,

153, 228

Turbulence, 66

surfer analogy, 32

Splitting-worlds, 134-135, 178, 233

Turing, Alan, 207

Spooky links, 31-32,

Turnbull, C. M., 121

38, 46, 49, 50-51,

53-54, 62, 129-132, 221,225-

Twistors, 200

226, 229

Two-slit experiments

Stalin, Josef,

atoms, 22

183-184

State space, 74-75, 76, 179 Statistics, 9, 26,

physicists’

balls, 13-14, 16, 21, 22,

27

buckeyballs, 86-87, 211-212, 213

40

surnames, 70

probability distinguished from, 61-

chickens, 23-24, 25, 27, 53-54 detectors, 27-28, 53 electrons, 23, 25

63 Steel, radioactive-free, 81

String theory,

bowling

1

16, 216,

243

Strong decoherence, 182, 230

of faster-than-light causality, 72 interference patterns, 23, 25, 86-87,

213, 222-224

Struldbruggs, 190-191, 257

light, 13-14,

19-21

Sturgeon analogy, 192-193

with one

closed, 142

Soul, 210

pilot waves, 20-21,

Suicide, 42, 186, 187, 188-189, 231, 232

single-photon, 19-21

Sunlight, 85

splitting worlds,

Supercooled

water, 14-15, 17, 21

slit

23-24

134-135

atoms, 165 water, 30-31

u

Surfer analogy, 21, 24, 25-26, 28-29, 34, 49, 54-55,

70,253

Swift, Jonathan, 190,

257

Uncertainty principle, 25-26, 29, 31, 90, 202

S'.

272-1 Index

Wavelength,

University of Heidelberg, 83

University of Vienna, 86, 206

150,

Weak

^

V

14, 21-22, 48-49, 54-55,

204,^13

decoherence, 182, 230 50, 55-56, 158-

Weather forecasting, 159,163,217 Weber,!., 198

Vacuum,

localization time, 85

Web

Vaidman, Lev, 140, 143, 169, 170, 175176, 195,229,

’t

also

1

Spooky

07,^224-225. See

links

Wheeler, John, 133, 135

Hooft, 246

Wigner, Eugene, 68-69

Vectors

World

Bloch sphere, 88-89

lines,

137

branching

defined, 117

of,

and personal

of entangled particles, 34-36

170-173, 174, 182 identity,

185-197

space-time curvature, 250

45

Verne, Jules,

250

Weirdness, 41-42,

236

Valentini, Antony, 72, 73

van

site,

Wormholes, 201

Victorian notions of ether, 245

Wynn, Karen, 108

von Neumann, John, 67-68, 199 Vonnegut, Kurt, 30-31

X

w

X-ray photons, 204

*

XOR,219, 220

Wallace, David, 154, 177, 184, 191

Warping of space-time,

1

10, 123,

201-

Y

202, 245

Wave. See also Guide waves; Pilot Young, Thomas,

waves

13,

14-15

electromagnetic, 110 interference, 14, 25, 149-150

mechanics, 13,

z

14, 17, 18, 58-59,

150-151 Zeh, Dieter, 83, 87

packets, 150-151, 152

Zeilinger,

probability, 75, 77-80 rider, 21, 24, 25-26, 28-29, 54-55,

169, 170,211-227, 228, 258

Informational Principle, 217, 222-

56, 70

226

tsunami analogy, 58

Zero-interaction detector, 140-154, 174

Wavefunction

Zero-probability outcomes, 134-135

multiverse, 135

random

Anton, 86-87, 144, 147-148,

collapse, 198-199

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